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

Let the series be  21, 21r, 21r2, ........
Sum =  $\frac{21}{1-r}$ is a positive integer
also 21r  is a positive integer
$S = \frac{\left(21\right)\left(21\right)}{21-21r}$ as   $21r \in N$  hence,  $21 – 21r$ must be an integer
also $21r < 21$
hence $21 – 21r$ may be equal to  1, 3, 7  or  9  (think!)
i.e.  must be a divisor of (21)(21) 
hence $21 – 21r = 1 or 3 or 7 or 9$
$21r = 20, 18, 14 or 12 Ans.$