Question

In a G.P nth term an = 2^n-1 then find common ratio.​

Answer 1

Answer:

Step-by-step explanation:

nth term of the G.P. is given to be 2^n. Setting n=1,2,3,…. we find that

First term of the G.P. is 2^1 = 2;

Second term of the G.P. is 2^2 = 4;

Third term of the G.P. is 2^3 = 8.

G.P. is, therefore 2,4,8,16,32,64,…..

For this G.P., first term a = 2, and common ratio r = 2.

Sum of the first n terms of a G.P. with first term “a” and common ratio “r” is given by

S = a(r^n - 1)/(r - 1).

To find the sum of first 6 terms of the G.P. with first term “2” and common ratio “2” , we set a = 2, r = 2, n = 6.

S = 2(2^6 - 1)/(2 - 1) = 2(64 - 1)/(1) = 2(63) = 126.

Sum of the first 6 terms of this G.P. is, therefore, 126.