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

Question

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1) th to (2n) th term is

Philoid · Accepted Answer

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

Sum of n terms =

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

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

Here,

a _n ₊₁ = ar^n+1–1 = arⁿ

∴ Required ratio =

∴ The ratio of the sum of first n terms of a G.P. to the sum of terms from

(n +1)th to (2n)th term is = .