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