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.

Asked by Abhisek | 1 year ago |  79

##### Solution :-

Given that the sum of some terms in a G.P is 315.

Let the number of terms be n.

We know that, sum of terms is

$$s_n=\dfrac{a(1-r^n)}{r-1}$$

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

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

2n-1=63

2= 64 = (2)6

n=6

Hence, the last term of the G.P = 6th term = ar6 – 1 = (5)(2)5 = (5)(32) = 160

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

Answered by Pragya Singh | 1 year ago

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