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2015-04-01T13:52:53+05:30

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N=5
for a geometric progression, the nth term is a(r)^n-1. a is the first term. r is the common ratio.
so,
A(R)^n-1 = a(r)^n-1
A=162, R=54/162 for the 1st geometric progression.
a=2/81, r= (2/27)/(2/81) for the 2nd geometric progression.
solve and get the value for n.

hope this helped!
still, if you are having doubt, ask me where u couldn't understand n i will help :)
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2015-04-01T15:55:58+05:30

This Is a Certified Answer

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
There are two geometric progressions. 
The nth term of both are same.

for 162,54,18...
a = 162, r = 54/162 = 1/3
for 2/81, 2/27, 2/9...
a = 2/81, r = (2/27) / (2/81) = 81/27 = 3

162 \times  \frac{1}{3^{n-1}} = \frac{2}{81} \times 3^{n-1}\\ \\ \frac{162}{3^{n-1}} = \frac{2 \times 3^{n-1}}{81}\\ \\2 \times 3^{2(n-1)}=162 \times 81 \\ \\2 \times 3^{2(n-1)}=2 \times 81 \times 81 \\ \\2 \times 3^{2(n-1)}=2 \times 3^4 \times 3^4=2 \times 3^8\\ \\3^{2(n-1)}= 3^8\\ \\2(n-1)=8\\ \\n-1= \frac{8}{2}=4\\ \\n=4+1=\boxed{5}


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