What is the sum of n terms of the series 1, 4, 9, 16, 25, 36 . Theyare not in AP or GP.

You are absolutely right. The series given is not an AP or
a GP as neither is the difference between consecutive terms common nor is the ratio of
consecutive terms the same. But if you notice carefully the series is just made up by
the squares of consecutive numbers. 1= 1^2 , 4= 2^2 , 9= 3^3, 16= 4^2 , 25= 5^2 and so
on.

Now the relation for the sum of the first n squares is
given by the relation: n*(n+1)*(2n+1) / 6

Therefore the sum
of the first n terms of the series is

= n*(n+1)*(2n+1) /
6.