Find the number of terms in the following G.P. (i) 4, 8, 16,…,8192 ?

Find the number of terms in the following G.P.

(i) 4, 8, 16,…,8192 ?

Solution :

Let nth term be "8192"

tn  = 8192

a = 4, r = 8/4  = 2

 ar n -1  =  8192

4(2)n -1  =  8192

22(2)n -1  =  8192

2 n+1  = 213

n + 1  = 13

n = 12

Hence the 12th term of the above geometric sequence is 8192.

Hence there are 12 terms in the given G.P.