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 - rⁿ)/(1 - r)

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

Hence,

315 = 5(2ⁿ - 1)/(2 - 1)

⇒ 2ⁿ - 1 = 63

⇒ 2ⁿ = 64 = (2)⁶

⇒ n = 6

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

a₆ = ar^{6 - 1}

= ar⁵

= 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