Question

If the first term of a G.P. is 2 and sum to infinity is 6. Find the common ratio.

Answer 1

➡️ Solution:

As we know that sum of infinite terms of a GP is given by

$S_{∞} = \frac{a}{1 - r}$
here a is the first term and r is common ratio

Given that

a = 2

S∞= 6

$6 = \frac{2}{1 - r} \\ \\ 6(1 - r) = 2 \\ \\ 1 - r = \frac{1}{3} \\ \\ r = 1 - \frac{1}{3} \\ \\ r = \frac{3 - 1}{3} \\ \\ r = \frac{2}{3}$
Hope it helps you.