1.

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 :

Answer»

`1/4`
`1/8`
`1/16`
`1/32`

SOLUTION :Let the G.P. be, a, ar , `ar^2`
`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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