document.write( "Question 1112262: The sum of the first two terms of a geometric progression is 5/2,and the sum of the first four teems is 65/18,find the third term of the G.P if r is greater than 0 \n" ); document.write( "
Algebra.Com's Answer #727270 by greenestamps(13209)\"\" \"About 
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\n" ); document.write( "The sum of the first two terms is 5/2, and the sum of the first four terms is 65/18. So the sum of the 3rd and 4th terms is
\n" ); document.write( "\"65%2F18-5%2F2+=+65%2F18-45%2F18+=+20%2F18+=+10%2F9\".

\n" ); document.write( "The third term is the first term multiplied by the common ratio r twice; the fourth term is the second term multiplied by r twice. So the sum of the third and fourth terms is the sum of the first two terms, multiplied by the common ratio twice:
\n" ); document.write( "\"10%2F9+=+%285%2F2%29%28r%5E2%29\"
\n" ); document.write( "\"r%5E2+=+%2810%2F9%29%2F%285%2F2%29+=+%2810%2F9%29%2A%282%2F5%29+=+20%2F45+=+4%2F9\"
\n" ); document.write( "\"r+=+2%2F3\" because the problem says r is positive

\n" ); document.write( "The fourth term is the third term multiplied by r=2/3; so the sum of the third and fourth terms is the third term plus 2/3 of the third term:
\n" ); document.write( "\"10%2F9+=+t3+%2B+%282%2F3%29t3+=+%285%2F3%29t3\"
\n" ); document.write( "\"t3+=+%2810%2F9%29%2F%285%2F3%29+=+%2810%2F9%29%2A%283%2F5%29+=+6%2F9+=+2%2F3\"

\n" ); document.write( "Answer: The third term of the sequence is 2/3.

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\n" ); document.write( "Having posted that solution, I see there is what I think is a slightly easier way to find the common ratio....

\n" ); document.write( "Since the third term is the first term multiplied by the common ratio r twice and the fourth term is the second term multiplied by r twice, the sum of the first four terms is the sum of the first two terms, plus the sum of the first two terms multiplied by r twice:

\n" ); document.write( "\"65%2F18+=+%285%2F2%29%2B%285%2F2%29%2Ar%5E2+=+%285%2F2%29%281%2Br%5E2%29\"
\n" ); document.write( "\"1%2Br%5E2+=+%2865%2F18%29%2F%285%2F2%29+=+%2865%2F18%29%2A%282%2F5%29+=+13%2F9\"
\n" ); document.write( "\"r%5E2+=+4%2F9\"
\n" ); document.write( "\"r+=+2%2F3\"

\n" ); document.write( "Then from there proceed as in the earlier solution I showed. \n" ); document.write( "
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