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.