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The sum of an infinity decreasing G.P is equal to 4 and the sum of the cubes of its terms is equal to 64/. Then 5^(th) term of the progression is : |
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Answer» `1/4` `implies(a)/(1-r) =4 ""….(1)` ALSO, `a^3 + (ar)^3 + ………. = (a^3)/(1-r^3) implies(a^3)/(1-r^3)=(64)/(7)` `implies7a^3 = 64 (1-r^3) ""….(2)` USING (1) and (2) , we have `7 xx 64 (1-r)^3 = 64(1-r^3) implies2r^2 - 5R + 2 = 0impliesr=1//2,2` `therefore ` G.P. is decreasing `impliesr=1//2 ` and a=2 |
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