Complete the series 1,6,13,22,33,..49514648

The given series is: 1, 6, 13, 22, 33, ...

This appears to be a series of consecutive perfect squares plus one.

The pattern is as follows:

1^2 + 1 = 2 2^2 + 2 = 6 3^2 + 3 = 13 4^2 + 4 = 22 5^2 + 5 = 33

So, the nth term of the series can be given by the formula n^2 + n.

To find the next term in the series, we need to find the value of n that makes n^2 + n = 49514648.

Solving this equation for n, we get:

n^2 + n - 49514648 = 0

This is a quadratic equation, and we can solve it using the quadratic formula:

n = [-1 + sqrt(1 + 449514648)] / 2 or n = [-1 - sqrt(1 + 449514648)] / 2

The positive root of this equation will give us the value of n.

Once we have the value of n, we can find the next term in the series by plugging n into the formula n^2 + n.