Question

1. Find the missing number in the series:
(i) 5, 8, 10, 10, 15, 12, 20, ?
(ii) 2, 7, 26, 111, ?, 3395
(iii) 2, 9, 28, 65, ?

Answer 1

Other answers follow (n^3 + 1) pattern. Interestingly, for some reasons, it did not occur to me at first. Rather I ended up doing this following pattern.

I split the series into,

(2 * 1), (3 * 3), (4 * 7), (5 * 13), (6 * ?), ( 7 * 31)…

And then, I arrived at this pattern .. (N+1) * [(N * (N-1)) + 1]..

i.e, for N=6, it is 7* [(6*5)+1] = 217.. And for N=1, it is 2 * [(1*0)+1]..

And hence, I calculated for N=5.. the value is 126..