Can anybody help me in finding what is the next number in the above series and the logic behind it ?
You understand, I hope, that knowing a few numbers in a sequence does NOT require that the rest of the sequence be anything in particular? What they are really asking is "what is the simplest rule that will give these numbers?". And even that may be a matter of taste. For example, given any n numbers, there exist a polynomial, p(x), of degree n-1 that will give those values for x= 1, 2, ..., n. Here there exist a fourth degree polynomial that will give those values. Looking for something simpler, you might try subtracting or dividing consecutive terms but I don't see that that gives anything simple.