Find the number of terms in the following G.P. (ii) 1/3, 1/9, 1/27,................1/2187

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.