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.

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