document.write( "Question 26238: I am very frustrated. I am working on geometric series of numbers and thought that it would be easy but, I have not done this in a while and I have to admit that I am perplexed. Here is what I must solve:\r
\n" ); document.write( "\n" ); document.write( "Use the geometric series of numbers 1, 2, 4, 8,...to find the following:
\n" ); document.write( "a) What is r, the ratio between 2 consecutive terms?
\n" ); document.write( " (I got r=1)
\n" ); document.write( "b) Using the formula for the nth term of a geometric series, what it the 24th term?\r
\n" ); document.write( "\n" ); document.write( "c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?\r
\n" ); document.write( "\n" ); document.write( "Could you please help refresh my memory by showing me step by step how to complete this first set of problems? Thank you!!!!
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #14108 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
I am very frustrated. I am working on geometric series of numbers and thought\r\n" );
document.write( "that it would be easy but, I have not done this in a while and I have to admit\r\n" );
document.write( "that I am perplexed. Here is what I must solve: \r\n" );
document.write( "Use the geometric series of numbers 1, 2, 4, 8,...to find the following:\r\n" );
document.write( "a) What is r, the ratio between 2 consecutive terms?\r\n" );
document.write( "(I got r=1)\r\n" );
document.write( "\r\n" );
document.write( "NO! First of all this is a SEQUENCE, not a SERIES. A SEQUENCE has commas\r\n" );
document.write( "between its terms whereas a SERIES has plus signs between its terms.\r\n" );
document.write( "\r\n" );
document.write( "There are three ways to find r for this geometric SEQUENCE.  DIVIDE any term\r\n" );
document.write( "by the previous term.\r\n" );
document.write( "\r\n" );
document.write( "First way to get r:\r\n" );
document.write( "\r\n" );
document.write( "Divide the 2nd term by the 1st term. That is, 2 divided by 1 gives 2. So r=2\r\n" );
document.write( "\r\n" );
document.write( "Second way to get r:\r\n" );
document.write( "\r\n" );
document.write( "Divide the 3rd term by the 2nd term. That is, 4 divided by 2 gives 2. So r=2.\r\n" );
document.write( "\r\n" );
document.write( "Third way to get r:\r\n" );
document.write( "\r\n" );
document.write( "Divide the 4th term by the 3rd term. That is, 8 divided by 4 gives 2. So r=2. \r\n" );
document.write( "\r\n" );
document.write( "Now you know how to find the common ratio r.  I think you used SUBTRACTION,\r\n" );
document.write( "which is what you use with an ARITHMETIC sequence to find the common\r\n" );
document.write( "difference d, not common ratio r. You are getting a GEOMETRIC sequence\r\n" );
document.write( "confused with an ARITHMETIC sequence.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "b) Using the formula for the nth term of a geometric series, what it the 24th\r\n" );
document.write( "term?\r\n" );
document.write( "\r\n" );
document.write( "Again the word is SEQUENCE, not SERIES.  Use SEQUENCE when commas separate the\r\n" );
document.write( "terms.  Use SERIES when plus (or minus) signs separate the terms.\r\n" );
document.write( "\r\n" );
document.write( "The formula for the nth term of a geometric sequence is\r\n" );
document.write( "\r\n" );
document.write( "an = a1rn-1\r\n" );
document.write( "\r\n" );
document.write( "Here a1 = first term = 1, n = 24, r = 2\r\n" );
document.write( "\r\n" );
document.write( "a24 = (1)(2)24-1\r\n" );
document.write( "\r\n" );
document.write( "a24 = 223 = 8388608\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "c) Using the formula for the sum of a geometric series, what is the sum of the\r\n" );
document.write( "first 10 terms? \r\n" );
document.write( "\r\n" );
document.write( "Now you are correctly asking about a SERIES 1 + 2 + 4 + 8 + ···\r\n" );
document.write( "\r\n" );
document.write( "Sn = a1(rn-1)/(r-1)\r\n" );
document.write( "\r\n" );
document.write( "n = 10, a1 = 1, r = 2\r\n" );
document.write( "\r\n" );
document.write( "S10 = 1(210-1)/(2-1) = (210-1)/1 = 210-1 = 1024-1 = 1023\r\n" );
document.write( "\r\n" );
document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
\n" ); document.write( "
\n" );