Given:
1,5,25,61.....
To find:
The following number.
Solution:
We can see a pattern in the given sequence.
[tex](-1)^2+(0)^2=1+0=1[/tex]
[tex](1)^2+(2)^2=1+4=5[/tex]
[tex](3)^2+(4)^2=9+16=25[/tex]
[tex](5)^2+(6)^2=25+36=61[/tex]
Using this pattern the next term is the sum of squares of 7 and 8.
[tex](7)^2+(8)^2=49+64=113[/tex]
Therefore, the next number is 113.
