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

(N+1)^2 – N^2 = N^2 + 2N + 1 – N^2 = 2N + 1

The difference between two consecutive squares in 2N + 1. It’s an odd number which increases by 2 each time.