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Question
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
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Solution
a = (27)2
tn = arn–1
∴ t7 = ar6
∴ ar6 = 82
∴ r6 = `8^2/27^2 = 2^6/3^6`
∴ r = `2/3`
Sn = `("a"(1 - "r"^"n"))/(1 - "r")` for r < 1
∴ S8 = `((27)^2[1 - (2/3)^"s"])/(1 - 2/3)`
= `3.(27)^2 [(3^8 - 2^8)/3^8]`
= `3^7 ((6561 - 256))/3^8`
∴ S8 = `6305/3`
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