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The first term of an infinite geometric ...

The first term of an infinite geometric series is `21.` The second term and the sum of the series are both positive integers. Then which of the following is not the possible value of the second term a. `12` b. `14` c. `18` d. none of these

A

12

B

14

C

18

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Let the series be 21,21r,`21r^(2)`,…
Sum,`S=21/(1-r)` is a positive integer
also 21r is a positive integer
`S=((21)(21))/(21-21r)`
Since,21 r `ne`N,21-21r must be an integer. Also,21r`lt`21
Hence 21-21r may be equal to 1,3,7 or 9
i.e., must be a divisor of (21)(21)
Hence, 21-21r=1,3,7,9
Therefore ,21 r=20,18,14, or 12.
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