Question

the sum of some terms of GP is 315 whose first term and the common ratio are 5 and 12 find the last term and the number of terms​

Answer 1

Step-by-step explanation:

Hey there!

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

Sn \: = \: \frac{a(r^{n} \: - 1) }{r \: - \: 1}Sn=

r−1

a(r

n

−1)

We know that,

It is given that the first term a is 5 and common ratio r is 2.

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

2−1

5(2

n

−1)

{2}^{n} - 1 = 632

n

−1=63

n = 6n=6

∴ Last term of the G.P = 6th term

= {ar}^{6 - 1 } = (5)(2)^{5} = 160=ar

6−1

=(5)(2)

5

=160

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