# The sum of some terms of G.P is 315 whose first term and common ratio are 5 and 2 respectively. Find the last term and the number of terms

**Solution:**

Let the sum of n terms of the G.P be 315.

It is known that S_{n} = a (1 - r^{n})/(1 - r)

It is given that a = 5 and common ratio r = 2

Hence,

315 = 5(2^{n} - 1)/(2 - 1)

⇒ 2^{n} - 1 = 63

⇒ 2^{n} = 64 = (2)^{6}

⇒ n = 6

Therefore, the last term of the G.P. is 6^{th} term

a_{6} = ar^{6 }^{- }^{1}

= ar^{5}

= 5 x (2)^{5}

= 5 x 32

= 160

Thus, the last term of the G.P is 160

NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 8

## The sum of some terms of G.P is 315 whose first term and common ratio are 5 and 2 respectively. Find the last term and the number of terms.

**Summary:**

Given that the sum of some terms the G.P is 315 whose first term and common ratios are 5 and 2 respectively, the last term comes out to be 160 and n = 6