Question

1,5,25,61.....
What's following number? ​

Answer 1

Given:

1,5,25,61.....

To find:

The following number.

Solution:

We can see a pattern in the given sequence.

`(-1)^2+(0)^2=1+0=1`

`(1)^2+(2)^2=1+4=5`

`(3)^2+(4)^2=9+16=25`

`(5)^2+(6)^2=25+36=61`

Using this pattern the next term is the sum of squares of 7 and 8.

`(7)^2+(8)^2=49+64=113`

Therefore, the next number is 113.