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

(ii) 1/3, 1/9, 1/27,................1/2187

Solution :

Let nth term be "1/2187"

tn = 1/2187

a = 1/3, r = (1/9)/(1/3) = 1/3

ar n -1 = 1/2187

(1/3)(1/3)n -1 = 1/2187

(1/3)1 + n-1 = 1/2187

(1/3)n = (1/3)7

n = 7

Hence the 7th term of the above sequence is 1/2187.

Hence there are 7 terms in the given G.P.