Question

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

Answer 1

Let the sum of n terms of the G.P. be 315.
It is known that, $S_n = \frac{a(r^n - 1) }{ r - 1}$
It is given that the first term a is 5 and common ratio r is 2.
∴ $315 = \frac{5(2^n - 1) }{2 - 1}$
$⇒ 2^n - 1 = 63$
$⇒ 2n = 64 = (2)^6$
$⇒ n = 6$
∴ Last term of the G.P = 6th term = ar6-1 = (5)(2)5=(5) (32)=160
Thus, the last term of the G.P. is 160.