SOLUTION: The sum of first 3 terms is 37/8 and the sum of first 6 terms is 3367/512.find the first term and common ratio.

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Question 1148035: The sum of first 3 terms is 37/8 and the sum of first 6 terms is 3367/512.find the first term and common ratio.
Answer by greenestamps(13203) About Me  (Show Source):
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The sum of the first three terms is 37/8:
a%2Bar%2Bar%5E2+=+37%2F8

The sum of the first six terms is 3367/512:
a%2Bar%2Bar%5E2%2Bar%5E3%2Bar%5E4%2Bar%5E5+=+3367%2F512

The sum of terms 4 to 6 is the difference, 3367/512-37/8:
ar%5E3%2Bar%5E4%2Bar%5E5+=+3367%2F512-37%2F8+=+3367%2F512-2368%2F512+=+999%2F512

The sum of terms 4 to 6 is the sum of the first three terms, multiplied by r^3. That is,
ar%5E3%2Bar%5E4%2Bar%5E5+=+r%5E3%28a%2Bar%2Bar%5E2%29
999%2F512+=+r%5E3%2837%2F8%29
r%5E3+=+%28999%2F512%29%2A%288%2F37%29+=+27%2F64
r+=+3%2F4

The sum of the first three terms is 37/8:
a%2B%283%2F4%29a%2B%289%2F16%29a+=+37%2F8
%2837%2F16%29a+=+37%2F8
a+=+2

ANSWERS: first term 2; common ratio 3/4