Why is every square number the difference between the previous 2 plus 2?

Question

Hard to explain but like 1 squared is 1
2 is 4 that’s 3 difference
3 squared is 9 that’s a 5 difference
4 is 16 that’s a 7 difference. It just keeps rising by 2 why is this?

In: 5

Answer 1

To go from 1^2 to 2^2 you add 3 (1+2)

To go from 2^2 to 3^2 you add 5 (2+3)

To go from 10^2 to 11^2 you add 21 (10+11)

See the pattern? You add both consecutive numbers to the square of the first to get the square of the second. In general: n^2 to (n+1)^2 you add n and n+1. To go from (n+1)^2 to (n+2)^2 add n+1 and n+2, so the increase will be 2 each time.