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Question
Check whether the following sequence is G.P. If so, write tn.
2, 6, 18, 54, …
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Solution
2, 6, 18, 54, …
t1 = 2, t2 = 6, t3 = 18, t4 = 54, …
Here, `"t"_2/"t"_1 = "t"_3/"t"_2 = "t"_4/"t"_3` = 3
∵ the ratio of any two consecutive terms is a constant, hence the given sequence is a Geometric progression.
Here, a = 2, r = 3
tn = arn–1
∴ tn = 2(3n–1)
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