john212/index.html

## index.html
<!DOCTYPE html>
<html>
<head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width">
  <title>Arithmetic and Geometric Sequence and Series</title>
</head>
<body>
<P>A program that will identify and then solve Arithmetic and Geometric Sequences and Series<br>
after the user inputs the first three terms, a desired unknown term to be calculated,<br>
and a starting and ending term for finding the sum of the related series.</P>

<P>The Arithmetic Sequence and Series Formulas used are:
<UL>
<LI>a<sub>n</sub> = a<sub>1</sub> + (n -1)*d where d = common difference</LI>
<LI>S<sub>n</sub> = (n/2)(a<sub>1</sub> + a<sub>n</sub>)</LI>
</UL>
</P>

<P>The Geometric Sequence and Series Formulas used are:
<UL>
<!-- Symbols used:  &#8734; = infinity &#60; = less than-->
<LI>a<sub>n</sub> = a<sub>1</sub> * r<sup>n-1</sup> where r = common ratio</LI>
<LI>S<sub>n</sub> = a<sub>1</sub> * (1-r<sup>n</sup>)/(1-r)</LI>
<LI>S<sub>&#8734;</sub> = a<sub>1</sub> * (1)/(1-r), where -1&#60;r&#60;1</LI>
</UL>
</P>

<P>This program is written in JavaScript.</P>

<P>By Mr. C. July 18, 2015</P>

<script type="text/javascript">


  </script>
<script id="jsbin-javascript">
// **** Description ****
// Write a program that will identify and then solve
// Arithmetic and Geometric Sequences and Series
// after the user inputs the first three terms.
// *********************

// **** Define and initialize variables ****
var a1 = "";          // first term of the sequence, input by user.
var a2 = "";          // second term of the sequence, input by user.
var a3 = "";          // third term of the sequence, input by user.
var n = "";           // any term of the sequence, input by user.
var an_arith = "";    // value of user requested nth term in arithmetic sequence.
var an_geo = "";      // value of user requested nth term in geometic sequence.
var n_start = "";     // start term for sum of series, input by user.
var n_end = "";       // end term for sum of series, input by user.
var a_start = "0.0";  // first term in finite series.
var a_end   = "0.0";  // last term in finite series.
var n_series = "0.0"; // number of terms in finite series.
var sum_arith = "0.0";   // finite sum of arithmetic series.
var sum_geo = "0.0";     // finite sum of geometric series.
var sum_inf_geo = "0.0"; // finite sum of infinite geometric series.
var d = 0.0;     // d = common difference of an arithmetic sequence , calculated.
var r = 0.0;     // r = common ratio of an arithmetic sequence, calculated.
var d12 = 0.0;   // test d, a1 + d12 =? a2 where d12 = a2-a1
var d23 = 0.0;   // test d, a2 + d23 =? a3 where d23 = a3-a2
var r12 = 0.0;   // test r, a1 * r12 =? a2 where r12 = a2/a1
var r23 = 0.0;   // test r, a2 * r23 =? a3 where r23 = a3/a2
var arithmetic = false; // Boolean, is the sequence arithmetic?
var geometric = false;  // Boolean, is the sequence geometric?
// *****************************************

// **** Collect user input via popup boxes ****
a1 = prompt("Enter the first term of the sequence", "Type the value here");
a2 = prompt("Enter the second term of the sequence", "Type the value here");
a3 = prompt("Enter the third term of the sequence", "Type the value here");
n = prompt("Enter the desired term number of the sequence", "Type the value here");
n_start = prompt("Enter the stating term number of the finite series to be summed", "Type the value here");
n_end = prompt("Enter the ending term number > starting number of the series to be summed", "Type the value here");
// ***************************************

// **** Convert user text input into decimal numbers ****
/*
The parseFloat("string") function returns a number,
where "string" is the string value you want to parse.
Leading and trailing spaces are allowed and will be ignored.
If the first non space character is not a sign (+ or -), numeral (0-9),
decimal point or an exponent, and cannot be converted to a number,
parseFloat returns NaN. While parsing after the first non space character,
if the function encounters a character other than a sign (+ or -),
numeral (0-9), a decimal point, or an exponent, it returns the value
up to that point and ignores that character and all subsequent characters.
*/
a1 = parseFloat(a1);
a2 = parseFloat(a2);
a3 = parseFloat(a3);
n = parseFloat(n);
n_start = parseFloat(n_start);
n_end = parseFloat(n_end);
// ***************************************************

// **** Determine if the sequence of three numbers is arithmetic ****
// Check if the same common difference d separates the three terms.
// Note built-in function Math.pow(base,exponent) raises a number to a power.
// example: d = Math.pow(b,2) - (4*a*c); for b*b-4ac
d12 = a2-a1;
d23 = a3-a2
if(d12 === d23)
  {
  arithmetic = true;
  d = d12; // if the sequence is arithmetic, set d = to d12 or d23.
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is arithmetic, d = ", d);
  }//end of d12===d23 if block
else
  {
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT arithmetic.");
  }

if(arithmetic == true)
  {
  // Calculate the user requested nth term.
  an_arith = a1 + (n - 1)* d;
  document.write("<P>The ", n, "th term is ", an_arith);
  // Calculate the user requested finite series.
  n_series = (n_end - n_start) + 1;
  a_start = a1 +(n_start - 1) * d;
  a_end = a1 +(n_end - 1) * d;
  sum_arith = (n_series/2)*(a_start + a_end);
  document.write("<P>The sum from arithmetic sequence term ", n_start, " to term ", n_end, " is ", sum_arith);
  }//end of arithmetic===true if block.

// ***************************************************
// **** Determine if the sequence of three numbers is geometric ****
// Check if the same common ratio r separates the three terms.
// Note built-in function Math.pow(base,exponent) raises a number to a power.
// example: d = Math.pow(b,2) - (4*a*c); for b*b-4ac
r12 = a2/a1;
r23 = a3/a2
if(r12 === r23)
  {
  geometric = true;
  r = r12; // if the sequence is geometic, set r = to r12 or r23.
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is geometric, r = ", r);
  }//end of r12===r23 if block
else
  {
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT geometric.");
  }

if(geometric == true)
  {
  // Calculate the user requested nth term.
  an_geo = a1 * (Math.pow(r,n-1));
  document.write("<P>The ", n, "th term is ", an_geo);
  // Calculate the user requested finite series.
  n_series = (n_end - n_start) + 1;
  a_start = a1 * (Math.pow(r,n_start-1));
  a_end = a1 * (Math.pow(r,n_end-1));
  sum_geo = a_start * ((1 - Math.pow(r,n_series))/(1 - r));
  document.write("<P>The sum from geometic sequence term ", n_start, " to term ", n_end, " is ", sum_geo);
  // Calculate the infinite geometric series if it exists.
  if(Math.abs(r) < 1)
      {
	  sum_inf_geo = a1 * 1/(1-r);
	  document.write("<P>Since -1 < r < 1 the sum of the infinite geometic series is ", sum_inf_geo);
	  }// end of -1<r<1 if block
   else
      {
	  document.write("<P>Since the absolute value of r is greater than 1, the sum of the infinite geometic series does not converge.");
	  }
 }//end of geometric===true if block.

// ***************************************************
</script>


<script id="jsbin-source-javascript" type="text/javascript">// **** Description ****
// Write a program that will identify and then solve
// Arithmetic and Geometric Sequences and Series
// after the user inputs the first three terms.
// *********************

// **** Define and initialize variables ****
var a1 = "";          // first term of the sequence, input by user.
var a2 = "";          // second term of the sequence, input by user.
var a3 = "";          // third term of the sequence, input by user.
var n = "";           // any term of the sequence, input by user.
var an_arith = "";    // value of user requested nth term in arithmetic sequence.
var an_geo = "";      // value of user requested nth term in geometic sequence.
var n_start = "";     // start term for sum of series, input by user.
var n_end = "";       // end term for sum of series, input by user.
var a_start = "0.0";  // first term in finite series.
var a_end   = "0.0";  // last term in finite series.
var n_series = "0.0"; // number of terms in finite series.
var sum_arith = "0.0";   // finite sum of arithmetic series.
var sum_geo = "0.0";     // finite sum of geometric series.
var sum_inf_geo = "0.0"; // finite sum of infinite geometric series.
var d = 0.0;     // d = common difference of an arithmetic sequence , calculated.
var r = 0.0;     // r = common ratio of an arithmetic sequence, calculated.
var d12 = 0.0;   // test d, a1 + d12 =? a2 where d12 = a2-a1
var d23 = 0.0;   // test d, a2 + d23 =? a3 where d23 = a3-a2
var r12 = 0.0;   // test r, a1 * r12 =? a2 where r12 = a2/a1
var r23 = 0.0;   // test r, a2 * r23 =? a3 where r23 = a3/a2
var arithmetic = false; // Boolean, is the sequence arithmetic?
var geometric = false;  // Boolean, is the sequence geometric?
// *****************************************

// **** Collect user input via popup boxes ****
a1 = prompt("Enter the first term of the sequence", "Type the value here");
a2 = prompt("Enter the second term of the sequence", "Type the value here");
a3 = prompt("Enter the third term of the sequence", "Type the value here");
n = prompt("Enter the desired term number of the sequence", "Type the value here");
n_start = prompt("Enter the stating term number of the finite series to be summed", "Type the value here");
n_end = prompt("Enter the ending term number > starting number of the series to be summed", "Type the value here");
// ***************************************

// **** Convert user text input into decimal numbers ****
/*
The parseFloat("string") function returns a number,
where "string" is the string value you want to parse.
Leading and trailing spaces are allowed and will be ignored.
If the first non space character is not a sign (+ or -), numeral (0-9),
decimal point or an exponent, and cannot be converted to a number,
parseFloat returns NaN. While parsing after the first non space character,
if the function encounters a character other than a sign (+ or -),
numeral (0-9), a decimal point, or an exponent, it returns the value
up to that point and ignores that character and all subsequent characters.
*/
a1 = parseFloat(a1);
a2 = parseFloat(a2);
a3 = parseFloat(a3);
n = parseFloat(n);
n_start = parseFloat(n_start);
n_end = parseFloat(n_end);
// ***************************************************

// **** Determine if the sequence of three numbers is arithmetic ****
// Check if the same common difference d separates the three terms.
// Note built-in function Math.pow(base,exponent) raises a number to a power.
// example: d = Math.pow(b,2) - (4*a*c); for b*b-4ac
d12 = a2-a1;
d23 = a3-a2
if(d12 === d23)
  {
  arithmetic = true;
  d = d12; // if the sequence is arithmetic, set d = to d12 or d23.
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is arithmetic, d = ", d);
  }//end of d12===d23 if block
else
  {
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT arithmetic.");
  }

if(arithmetic == true)
  {
  // Calculate the user requested nth term.
  an_arith = a1 + (n - 1)* d;
  document.write("<P>The ", n, "th term is ", an_arith);
  // Calculate the user requested finite series.
  n_series = (n_end - n_start) + 1;
  a_start = a1 +(n_start - 1) * d;
  a_end = a1 +(n_end - 1) * d;
  sum_arith = (n_series/2)*(a_start + a_end);
  document.write("<P>The sum from arithmetic sequence term ", n_start, " to term ", n_end, " is ", sum_arith);
  }//end of arithmetic===true if block.

// ***************************************************
// **** Determine if the sequence of three numbers is geometric ****
// Check if the same common ratio r separates the three terms.
// Note built-in function Math.pow(base,exponent) raises a number to a power.
// example: d = Math.pow(b,2) - (4*a*c); for b*b-4ac
r12 = a2/a1;
r23 = a3/a2
if(r12 === r23)
  {
  geometric = true;
  r = r12; // if the sequence is geometic, set r = to r12 or r23.
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is geometric, r = ", r);
  }//end of r12===r23 if block
else
  {
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT geometric.");
  }

if(geometric == true)
  {
  // Calculate the user requested nth term.
  an_geo = a1 * (Math.pow(r,n-1));
  document.write("<P>The ", n, "th term is ", an_geo);
  // Calculate the user requested finite series.
  n_series = (n_end - n_start) + 1;
  a_start = a1 * (Math.pow(r,n_start-1));
  a_end = a1 * (Math.pow(r,n_end-1));
  sum_geo = a_start * ((1 - Math.pow(r,n_series))/(1 - r));
  document.write("<P>The sum from geometic sequence term ", n_start, " to term ", n_end, " is ", sum_geo);
  // Calculate the infinite geometric series if it exists.
  if(Math.abs(r) < 1)
      {
	  sum_inf_geo = a1 * 1/(1-r);
	  document.write("<P>Since -1 < r < 1 the sum of the infinite geometic series is ", sum_inf_geo);
	  }// end of -1<r<1 if block
   else
      {
	  document.write("<P>Since the absolute value of r is greater than 1, the sum of the infinite geometic series does not converge.");
	  }
 }//end of geometric===true if block.

// ***************************************************</script></body>
</html>

## jsbin.jaxahix.js
// **** Description ****
// Write a program that will identify and then solve
// Arithmetic and Geometric Sequences and Series
// after the user inputs the first three terms.
// *********************

// **** Define and initialize variables ****
var a1 = "";          // first term of the sequence, input by user.
var a2 = "";          // second term of the sequence, input by user.
var a3 = "";          // third term of the sequence, input by user.
var n = "";           // any term of the sequence, input by user.
var an_arith = "";    // value of user requested nth term in arithmetic sequence.
var an_geo = "";      // value of user requested nth term in geometic sequence.
var n_start = "";     // start term for sum of series, input by user.
var n_end = "";       // end term for sum of series, input by user.
var a_start = "0.0";  // first term in finite series.
var a_end   = "0.0";  // last term in finite series.
var n_series = "0.0"; // number of terms in finite series.
var sum_arith = "0.0";   // finite sum of arithmetic series.
var sum_geo = "0.0";     // finite sum of geometric series.
var sum_inf_geo = "0.0"; // finite sum of infinite geometric series.
var d = 0.0;     // d = common difference of an arithmetic sequence , calculated.
var r = 0.0;     // r = common ratio of an arithmetic sequence, calculated.
var d12 = 0.0;   // test d, a1 + d12 =? a2 where d12 = a2-a1
var d23 = 0.0;   // test d, a2 + d23 =? a3 where d23 = a3-a2
var r12 = 0.0;   // test r, a1 * r12 =? a2 where r12 = a2/a1
var r23 = 0.0;   // test r, a2 * r23 =? a3 where r23 = a3/a2
var arithmetic = false; // Boolean, is the sequence arithmetic?
var geometric = false;  // Boolean, is the sequence geometric?
// *****************************************

// **** Collect user input via popup boxes ****
a1 = prompt("Enter the first term of the sequence", "Type the value here");
a2 = prompt("Enter the second term of the sequence", "Type the value here");
a3 = prompt("Enter the third term of the sequence", "Type the value here");
n = prompt("Enter the desired term number of the sequence", "Type the value here");
n_start = prompt("Enter the stating term number of the finite series to be summed", "Type the value here");
n_end = prompt("Enter the ending term number > starting number of the series to be summed", "Type the value here");
// ***************************************

// **** Convert user text input into decimal numbers ****
/*
The parseFloat("string") function returns a number,
where "string" is the string value you want to parse.
Leading and trailing spaces are allowed and will be ignored.
If the first non space character is not a sign (+ or -), numeral (0-9),
decimal point or an exponent, and cannot be converted to a number,
parseFloat returns NaN. While parsing after the first non space character,
if the function encounters a character other than a sign (+ or -),
numeral (0-9), a decimal point, or an exponent, it returns the value
up to that point and ignores that character and all subsequent characters.
*/
a1 = parseFloat(a1);
a2 = parseFloat(a2);
a3 = parseFloat(a3);
n = parseFloat(n);
n_start = parseFloat(n_start);
n_end = parseFloat(n_end);
// ***************************************************

// **** Determine if the sequence of three numbers is arithmetic ****
// Check if the same common difference d separates the three terms.
// Note built-in function Math.pow(base,exponent) raises a number to a power.
// example: d = Math.pow(b,2) - (4*a*c); for b*b-4ac
d12 = a2-a1;
d23 = a3-a2
if(d12 === d23)
  {
  arithmetic = true;
  d = d12; // if the sequence is arithmetic, set d = to d12 or d23.
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is arithmetic, d = ", d);
  }//end of d12===d23 if block
else
  {
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT arithmetic.");
  }

if(arithmetic == true)
  {
  // Calculate the user requested nth term.
  an_arith = a1 + (n - 1)* d;
  document.write("<P>The ", n, "th term is ", an_arith);
  // Calculate the user requested finite series.
  n_series = (n_end - n_start) + 1;
  a_start = a1 +(n_start - 1) * d;
  a_end = a1 +(n_end - 1) * d;
  sum_arith = (n_series/2)*(a_start + a_end);
  document.write("<P>The sum from arithmetic sequence term ", n_start, " to term ", n_end, " is ", sum_arith);
  }//end of arithmetic===true if block.

// ***************************************************
// **** Determine if the sequence of three numbers is geometric ****
// Check if the same common ratio r separates the three terms.
// Note built-in function Math.pow(base,exponent) raises a number to a power.
// example: d = Math.pow(b,2) - (4*a*c); for b*b-4ac
r12 = a2/a1;
r23 = a3/a2
if(r12 === r23)
  {
  geometric = true;
  r = r12; // if the sequence is geometic, set r = to r12 or r23.
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is geometric, r = ", r);
  }//end of r12===r23 if block
else
  {
  document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT geometric.");
  }

if(geometric == true)
  {
  // Calculate the user requested nth term.
  an_geo = a1 * (Math.pow(r,n-1));
  document.write("<P>The ", n, "th term is ", an_geo);
  // Calculate the user requested finite series.
  n_series = (n_end - n_start) + 1;
  a_start = a1 * (Math.pow(r,n_start-1));
  a_end = a1 * (Math.pow(r,n_end-1));
  sum_geo = a_start * ((1 - Math.pow(r,n_series))/(1 - r));
  document.write("<P>The sum from geometic sequence term ", n_start, " to term ", n_end, " is ", sum_geo);
  // Calculate the infinite geometric series if it exists.
  if(Math.abs(r) < 1)
      {
	  sum_inf_geo = a1 * 1/(1-r);
	  document.write("<P>Since -1 < r < 1 the sum of the infinite geometic series is ", sum_inf_geo);
	  }// end of -1<r<1 if block
   else
      {
	  document.write("<P>Since the absolute value of r is greater than 1, the sum of the infinite geometic series does not converge.");
	  }
 }//end of geometric===true if block.

// ***************************************************
	<!DOCTYPE html>
	<html>
	<head>
	<meta charset="utf-8">
	<meta name="viewport" content="width=device-width">
	<title>Arithmetic and Geometric Sequence and Series</title>
	</head>
	<body>
	<P>A program that will identify and then solve Arithmetic and Geometric Sequences and Series<br>
	after the user inputs the first three terms, a desired unknown term to be calculated,<br>
	and a starting and ending term for finding the sum of the related series.</P>

	<P>The Arithmetic Sequence and Series Formulas used are:
	<UL>
	<LI>a<sub>n</sub> = a<sub>1</sub> + (n -1)*d where d = common difference</LI>
	<LI>S<sub>n</sub> = (n/2)(a<sub>1</sub> + a<sub>n</sub>)</LI>
	</UL>
	</P>

	<P>The Geometric Sequence and Series Formulas used are:
	<UL>
	<!-- Symbols used: ∞ = infinity < = less than-->
	<LI>a<sub>n</sub> = a<sub>1</sub> * r<sup>n-1</sup> where r = common ratio</LI>
	<LI>S<sub>n</sub> = a<sub>1</sub> * (1-r<sup>n</sup>)/(1-r)</LI>
	<LI>S<sub>∞</sub> = a<sub>1</sub> * (1)/(1-r), where -1<r<1</LI>
	</UL>
	</P>

	<P>This program is written in JavaScript.</P>

	<P>By Mr. C. July 18, 2015</P>

	<script type="text/javascript">


	</script>
	<script id="jsbin-javascript">
	// ** Description **
	// Write a program that will identify and then solve
	// Arithmetic and Geometric Sequences and Series
	// after the user inputs the first three terms.
	// *********************

	// ** Define and initialize variables **
	var a1 = ""; // first term of the sequence, input by user.
	var a2 = ""; // second term of the sequence, input by user.
	var a3 = ""; // third term of the sequence, input by user.
	var n = ""; // any term of the sequence, input by user.
	var an_arith = ""; // value of user requested nth term in arithmetic sequence.
	var an_geo = ""; // value of user requested nth term in geometic sequence.
	var n_start = ""; // start term for sum of series, input by user.
	var n_end = ""; // end term for sum of series, input by user.
	var a_start = "0.0"; // first term in finite series.
	var a_end = "0.0"; // last term in finite series.
	var n_series = "0.0"; // number of terms in finite series.
	var sum_arith = "0.0"; // finite sum of arithmetic series.
	var sum_geo = "0.0"; // finite sum of geometric series.
	var sum_inf_geo = "0.0"; // finite sum of infinite geometric series.
	var d = 0.0; // d = common difference of an arithmetic sequence , calculated.
	var r = 0.0; // r = common ratio of an arithmetic sequence, calculated.
	var d12 = 0.0; // test d, a1 + d12 =? a2 where d12 = a2-a1
	var d23 = 0.0; // test d, a2 + d23 =? a3 where d23 = a3-a2
	var r12 = 0.0; // test r, a1 * r12 =? a2 where r12 = a2/a1
	var r23 = 0.0; // test r, a2 * r23 =? a3 where r23 = a3/a2
	var arithmetic = false; // Boolean, is the sequence arithmetic?
	var geometric = false; // Boolean, is the sequence geometric?
	// *****************************************

	// ** Collect user input via popup boxes **
	a1 = prompt("Enter the first term of the sequence", "Type the value here");
	a2 = prompt("Enter the second term of the sequence", "Type the value here");
	a3 = prompt("Enter the third term of the sequence", "Type the value here");
	n = prompt("Enter the desired term number of the sequence", "Type the value here");
	n_start = prompt("Enter the stating term number of the finite series to be summed", "Type the value here");
	n_end = prompt("Enter the ending term number > starting number of the series to be summed", "Type the value here");
	// ***************************************

	// ** Convert user text input into decimal numbers **
	/*
	The parseFloat("string") function returns a number,
	where "string" is the string value you want to parse.
	Leading and trailing spaces are allowed and will be ignored.
	If the first non space character is not a sign (+ or -), numeral (0-9),
	decimal point or an exponent, and cannot be converted to a number,
	parseFloat returns NaN. While parsing after the first non space character,
	if the function encounters a character other than a sign (+ or -),
	numeral (0-9), a decimal point, or an exponent, it returns the value
	up to that point and ignores that character and all subsequent characters.
	*/
	a1 = parseFloat(a1);
	a2 = parseFloat(a2);
	a3 = parseFloat(a3);
	n = parseFloat(n);
	n_start = parseFloat(n_start);
	n_end = parseFloat(n_end);
	// ***************************************************

	// ** Determine if the sequence of three numbers is arithmetic **
	// Check if the same common difference d separates the three terms.
	// Note built-in function Math.pow(base,exponent) raises a number to a power.
	// example: d = Math.pow(b,2) - (4ac); for b*b-4ac
	d12 = a2-a1;
	d23 = a3-a2
	if(d12 === d23)
	{
	arithmetic = true;
	d = d12; // if the sequence is arithmetic, set d = to d12 or d23.
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is arithmetic, d = ", d);
	}//end of d12===d23 if block
	else
	{
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT arithmetic.");
	}

	if(arithmetic == true)
	{
	// Calculate the user requested nth term.
	an_arith = a1 + (n - 1)* d;
	document.write("<P>The ", n, "th term is ", an_arith);
	// Calculate the user requested finite series.
	n_series = (n_end - n_start) + 1;
	a_start = a1 +(n_start - 1) * d;
	a_end = a1 +(n_end - 1) * d;
	sum_arith = (n_series/2)*(a_start + a_end);
	document.write("<P>The sum from arithmetic sequence term ", n_start, " to term ", n_end, " is ", sum_arith);
	}//end of arithmetic===true if block.

	// ***************************************************
	// ** Determine if the sequence of three numbers is geometric **
	// Check if the same common ratio r separates the three terms.
	// Note built-in function Math.pow(base,exponent) raises a number to a power.
	// example: d = Math.pow(b,2) - (4ac); for b*b-4ac
	r12 = a2/a1;
	r23 = a3/a2
	if(r12 === r23)
	{
	geometric = true;
	r = r12; // if the sequence is geometic, set r = to r12 or r23.
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is geometric, r = ", r);
	}//end of r12===r23 if block
	else
	{
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT geometric.");
	}

	if(geometric == true)
	{
	// Calculate the user requested nth term.
	an_geo = a1 * (Math.pow(r,n-1));
	document.write("<P>The ", n, "th term is ", an_geo);
	// Calculate the user requested finite series.
	n_series = (n_end - n_start) + 1;
	a_start = a1 * (Math.pow(r,n_start-1));
	a_end = a1 * (Math.pow(r,n_end-1));
	sum_geo = a_start * ((1 - Math.pow(r,n_series))/(1 - r));
	document.write("<P>The sum from geometic sequence term ", n_start, " to term ", n_end, " is ", sum_geo);
	// Calculate the infinite geometric series if it exists.
	if(Math.abs(r) < 1)
	{
	sum_inf_geo = a1 * 1/(1-r);
	document.write("<P>Since -1 < r < 1 the sum of the infinite geometic series is ", sum_inf_geo);
	}// end of -1<r<1 if block
	else
	{
	document.write("<P>Since the absolute value of r is greater than 1, the sum of the infinite geometic series does not converge.");
	}
	}//end of geometric===true if block.

	// ***************************************************
	</script>



	<script id="jsbin-source-javascript" type="text/javascript">// ** Description **
	// Write a program that will identify and then solve
	// Arithmetic and Geometric Sequences and Series
	// after the user inputs the first three terms.
	// *********************

	// ** Define and initialize variables **
	var a1 = ""; // first term of the sequence, input by user.
	var a2 = ""; // second term of the sequence, input by user.
	var a3 = ""; // third term of the sequence, input by user.
	var n = ""; // any term of the sequence, input by user.
	var an_arith = ""; // value of user requested nth term in arithmetic sequence.
	var an_geo = ""; // value of user requested nth term in geometic sequence.
	var n_start = ""; // start term for sum of series, input by user.
	var n_end = ""; // end term for sum of series, input by user.
	var a_start = "0.0"; // first term in finite series.
	var a_end = "0.0"; // last term in finite series.
	var n_series = "0.0"; // number of terms in finite series.
	var sum_arith = "0.0"; // finite sum of arithmetic series.
	var sum_geo = "0.0"; // finite sum of geometric series.
	var sum_inf_geo = "0.0"; // finite sum of infinite geometric series.
	var d = 0.0; // d = common difference of an arithmetic sequence , calculated.
	var r = 0.0; // r = common ratio of an arithmetic sequence, calculated.
	var d12 = 0.0; // test d, a1 + d12 =? a2 where d12 = a2-a1
	var d23 = 0.0; // test d, a2 + d23 =? a3 where d23 = a3-a2
	var r12 = 0.0; // test r, a1 * r12 =? a2 where r12 = a2/a1
	var r23 = 0.0; // test r, a2 * r23 =? a3 where r23 = a3/a2
	var arithmetic = false; // Boolean, is the sequence arithmetic?
	var geometric = false; // Boolean, is the sequence geometric?
	// *****************************************

	// ** Collect user input via popup boxes **
	a1 = prompt("Enter the first term of the sequence", "Type the value here");
	a2 = prompt("Enter the second term of the sequence", "Type the value here");
	a3 = prompt("Enter the third term of the sequence", "Type the value here");
	n = prompt("Enter the desired term number of the sequence", "Type the value here");
	n_start = prompt("Enter the stating term number of the finite series to be summed", "Type the value here");
	n_end = prompt("Enter the ending term number > starting number of the series to be summed", "Type the value here");
	// ***************************************

	// ** Convert user text input into decimal numbers **
	/*
	The parseFloat("string") function returns a number,
	where "string" is the string value you want to parse.
	Leading and trailing spaces are allowed and will be ignored.
	If the first non space character is not a sign (+ or -), numeral (0-9),
	decimal point or an exponent, and cannot be converted to a number,
	parseFloat returns NaN. While parsing after the first non space character,
	if the function encounters a character other than a sign (+ or -),
	numeral (0-9), a decimal point, or an exponent, it returns the value
	up to that point and ignores that character and all subsequent characters.
	*/
	a1 = parseFloat(a1);
	a2 = parseFloat(a2);
	a3 = parseFloat(a3);
	n = parseFloat(n);
	n_start = parseFloat(n_start);
	n_end = parseFloat(n_end);
	// ***************************************************

	// ** Determine if the sequence of three numbers is arithmetic **
	// Check if the same common difference d separates the three terms.
	// Note built-in function Math.pow(base,exponent) raises a number to a power.
	// example: d = Math.pow(b,2) - (4ac); for b*b-4ac
	d12 = a2-a1;
	d23 = a3-a2
	if(d12 === d23)
	{
	arithmetic = true;
	d = d12; // if the sequence is arithmetic, set d = to d12 or d23.
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is arithmetic, d = ", d);
	}//end of d12===d23 if block
	else
	{
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT arithmetic.");
	}

	if(arithmetic == true)
	{
	// Calculate the user requested nth term.
	an_arith = a1 + (n - 1)* d;
	document.write("<P>The ", n, "th term is ", an_arith);
	// Calculate the user requested finite series.
	n_series = (n_end - n_start) + 1;
	a_start = a1 +(n_start - 1) * d;
	a_end = a1 +(n_end - 1) * d;
	sum_arith = (n_series/2)*(a_start + a_end);
	document.write("<P>The sum from arithmetic sequence term ", n_start, " to term ", n_end, " is ", sum_arith);
	}//end of arithmetic===true if block.

	// ***************************************************
	// ** Determine if the sequence of three numbers is geometric **
	// Check if the same common ratio r separates the three terms.
	// Note built-in function Math.pow(base,exponent) raises a number to a power.
	// example: d = Math.pow(b,2) - (4ac); for b*b-4ac
	r12 = a2/a1;
	r23 = a3/a2
	if(r12 === r23)
	{
	geometric = true;
	r = r12; // if the sequence is geometic, set r = to r12 or r23.
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is geometric, r = ", r);
	}//end of r12===r23 if block
	else
	{
	document.write("<P>The sequence ", a1, ", ", a2, ", ", a3, ", ", "is NOT geometric.");
	}

	if(geometric == true)
	{
	// Calculate the user requested nth term.
	an_geo = a1 * (Math.pow(r,n-1));
	document.write("<P>The ", n, "th term is ", an_geo);
	// Calculate the user requested finite series.
	n_series = (n_end - n_start) + 1;
	a_start = a1 * (Math.pow(r,n_start-1));
	a_end = a1 * (Math.pow(r,n_end-1));
	sum_geo = a_start * ((1 - Math.pow(r,n_series))/(1 - r));
	document.write("<P>The sum from geometic sequence term ", n_start, " to term ", n_end, " is ", sum_geo);
	// Calculate the infinite geometric series if it exists.
	if(Math.abs(r) < 1)
	{
	sum_inf_geo = a1 * 1/(1-r);
	document.write("<P>Since -1 < r < 1 the sum of the infinite geometic series is ", sum_inf_geo);
	}// end of -1<r<1 if block
	else
	{
	document.write("<P>Since the absolute value of r is greater than 1, the sum of the infinite geometic series does not converge.");
	}
	}//end of geometric===true if block.

	// ***************************************************</script></body>
	</html>