document.write( "Question 392679: A geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum of infinity is 27. Find the value of
\n" ); document.write( "(a) The common ratio;\r
\n" ); document.write( "\n" ); document.write( "(b) The first term;\r
\n" ); document.write( "\n" ); document.write( "Thank you :)
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Algebra.Com's Answer #278731 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Hi
\n" ); document.write( "sum of the first two terms is 15 for a geometric series
\n" ); document.write( "\"a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29\", where r is the common ratio
\n" ); document.write( "\"a%5B2%5D+=+a%5B1%5D%2Ar+\"
\n" ); document.write( "\"a%5B1%5D%2Ba%5B2%5D+=+15+=+a%5B1%5D+%2B+a%5B1%5D%2Ar+=+a%5B1%5D%281+%2B+r%29\"
\n" ); document.write( "\"15+=+a%5B1%5D%28r%2B1%29\"
\n" ); document.write( "\"a%5B1%5D=+15%2F%281%2Br%29\"
\n" ); document.write( "\"S%5Bn%5D+=+27+=+a%5B1%5D%2F%281-r%29\"
\n" ); document.write( " \"27+=+%2815%2F%281%2Br%29%29+%2F%281-r%29\"
\n" ); document.write( " 27 = 15/(1-r^2)
\n" ); document.write( "1-r^2 = 15/27
\n" ); document.write( " r^2 = 12/27 = 4/9
\n" ); document.write( " r = 2/3 sequence has all positive terms..tossing out negative solution for r\r
\n" ); document.write( "\n" ); document.write( "(b) The first term;
\n" ); document.write( " \"15+=+a%5B1%5D%281%2B2%2F3%29\"
\n" ); document.write( " \"15+=+a%5B1%5D%2A%285%2F3%29\"
\n" ); document.write( " \"%283%2F5%29%2A15+=+a%5B1%5D\"
\n" ); document.write( " \"9+=+a%5B1%5D\" \n" ); document.write( "
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