document.write( "Question 1120323: For a geometric series, S2 = 20 and S3= 65. Find the first 3 terms. \n" ); document.write( "

Algebra.Com's Answer #735998 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The first tutor found the solution with a positive constant ratio between terms; it can be found using a little educated trial and error and some mental arithmetic.

\n" ); document.write( "Tutor @ikleyn showed there are two solutions.

\n" ); document.write( "Here is a different approach to find both solutions.

\n" ); document.write( "Since S2 = 20 and S3 = 65, we know T3 = 45. So
\n" ); document.write( " $\"S2+=+a%2Bar+=+20\"$
\n" ); document.write( " $\"T3+=+ar%5E2+=+45\"$

\n" ); document.write( "Then

\n" ); document.write( " $\"%28a%2Bar%29%2F%28ar%5E2%29+=+20%2F45+=+4%2F9\"$
\n" ); document.write( " $\"%281%2Br%29%2Fr%5E2+=+4%2F9\"$
\n" ); document.write( " $\"4r%5E2+=+9r%2B9\"$
\n" ); document.write( " $\"4r%5E2-9r-9+=+0\"$
\n" ); document.write( " $\"%284r%2B3%29%28r-3%29+=+0\"$

\n" ); document.write( "And we have what we need to find both solutions, one with r = -3/4 and one with r = 3.

\n" ); document.write( "T3 = 45 and r = 3 gives us the first three terms as 5, 15, and 45;
\n" ); document.write( "T3 = 45 and r = -3/4 gives us the first three terms as 80, -60, and 45. \n" ); document.write( "

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