The first term of an infinite geometric series is 21. The seconds term and the sum of the series are both positive integers. The possible value(s) of the second term can be

Options

A. 12
B. 14
C. 18
D. none of these

Answer

D

Explanation

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.