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.