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Question
If the first term of the G.P. is 6 and its sum to infinity is `96/17` find the common ratio.
Solution
Let a be the first term, r be the common ratio and S be the sum to infinity of the G.P.
Then S = `"a"/(1 - "r")`, where S = `96/17` and a = 6
∴ `96/17 = 6/(1 - r)`
∴ 1 – r × 96 = 6 × 17
∴ 1 – r = `(6 xx 17)/96`
∴ 1 – r = `17/16`
∴ 16 − 16r = 17
∴ 16r = 16 − 17
r = `-1/16`
Hence, the common ratio = `-1/16`.
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