Apr 09
Topic : Geometric Progression
Problem : The fourth term of a G.P. is 9 and the ninth term is 2,187. Find the first 4 terms of the G.P.
Solution :
Let the G.P. be a, ar, ar2 , ar3, …
T4 = ar3 = 9 ———- (1)
T8 = ar8 = 2,187 —— (2)
(2) ¸(1) : ar8 / ar3 = 2187/9
r5 = 243
r5 = 35
r = 3
Substitute r = 3 into (1): a(33) = 9
a = 1/3
Therefore the first four terms of the G.P. are 1/3, 1/3(3), 1/3(3)2, 1/3(3)3,
ie 1/3, 1, 3, 9
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