Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from .

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Solution

Let a be the first term and r be the common ratio of the G.P.

Since there are n terms from (n +1)^th to (2n)^th term,

Sum of terms from(n + 1)^th to (2n)^th term

a ⁿ⁺¹ = ar ^{n + 1} ^{– 1} = arⁿ

Thus, required ratio =

Thus, the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^th to (2n)^thterm is^.

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