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Question

Which term of the following sequences :
(a) 2,22,4,...is128?
(b) 3,3,33,... is 729?
(c) 13,19,127,... is 119683?

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Solution

(a) The given sequence is, 2,22,4,...
Clearly given sequence is in G.P
With a=2 and r=222=2
Let the nth term of the given sequence be 128.
an=arn1(2)(2)n1=128(2)(2)n12=(2)7(2)n12+1=(2)7n12=6n1=12n=13
Thus, the 13th term of the given sequence is 128.

(b) The given sequence is 3,3,33
Clearly this sequence is in G.P
with, a=3 and r=33=3
Let the nth term of the given sequence be 729.
an=arn1arn1=729(3)(3)n1=729(3)12(3)n12=(3)612+n12=61+n12=6n=12
Thus, the 12th term of the given sequence is 729.

(c) The given sequence is, 13,19,127,...
Clearly this sequence is in G.P
With a=13 and r=19÷13=13
Let the nth term of the given sequence be119683
an=arn1arn1=119683(13)(13)n1=119683(13)n=(13)9n=9
Thus, the 9th term of the given sequence is 119683

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