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Question
For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
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Solution
Let a be the first term and r be the common ratio of G.P.
Then S3 = 125 and S6 =125 + 27 = 152
∴ `"S"_6/"S"_3= 152/125`
∴ `([("a"("r"^6 - 1))/("r" - 1)])/([("a"("r"^3 - 1))/("r" - 1)]) = 152/125`
∴ `("r"^6 - 1)/("r"^3 - 1) = 152/125`
∴ `(("r"^3 - 1)("r"^3 + 1))/("r"^3 - 1) = 152/125`
∴ r3 + 1 = `152/125`
∴ r3 = `152/125 - 1 = 27/125 = (3/5)^3`
∴ r = `3/5`
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