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Question
Verify whether the following sequence is G.P. If so, write tn:
1, – 5, 25, – 125, ...
Solution
1, – 5, 25, – 125, ...
t1 = 1, t2 = – 5, t3 = 25, t4 = –125, …
Here, `"t"_2/"t"_1 = "t"_3/"t"_2 = "t"_4/"t"_3` = – 5
Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression.
Here, a = 1, r = – 5
tn = arn–1
∴ tn = (– 5)n–1
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