Question

For a G.P. a=3,r=2, Sn =765, find n.​

Answer 1

Answer: 8

Step-by-step explanation:

Answer 2

Given:

In a Geometric progression the value of a is 3, The common ratio is 2, and the sum of n terms is 765.

To Find:

The value of n is?

Solution:

The given problem can be solved using the concepts of Geometric Progression.

1. Consider a G.P with first term a, common ratio r, and the number of terms n. The sum of the first n terms of the G.P is,

=>$S_{n} = \frac{a(r^n - 1)}{(r-1)}$,

2. Use the above formula to find the value of n,

=> 765 = 3(2^n - 1)/(2-1),

=> 765 = 3(2^n - 1)/1,

=> 765 = 3(2^n - 1),

=> 3 x 255 = (2^n-1),

=> 255 = 2^n - 1,

=> 2^n = 256,

=> 2^n = 2^8,

=> n = 8.

3. The value of n is 8.

Therefore, the number of terms used to find the sum of the G.P is 8. The value of n is 8.