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Question

Which term of the series 2,23,229,......... is 162187?


A

10thterm

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B

8thterm

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C

9thterm

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D

11thterm

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Solution

The correct option is B

8thterm


Step 1: Note the given data

The common ratio of a GP series is anan-1.

Where anis a nthterm of the GP and an-1is a n-1thterm of the GP.

The series is 2,23,229,......

The ratio of the second term to the first term is 232=23.

The ratio of the third term to the second term is 22923=23.

The given series is in geometric progression the common ratio r=23.

a=2;an=162187

Step 2: Find the value of n

Geometric progression is a series of numbers where the ratio of two consecutive terms remains constant.

The formula to find the nthterm of a geometric progression is an=arn-1

162187=2×23n-1

162187=23n-1n

162187=323nn

166561=23nn

2438=212n3n

n=8ifam=an,thenm=n

Hence, the correct option is B.


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