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

Let n be any natural number. Then the square of n is n^2. The difference between n^2 and (n + 1)^2 is (n + 1)^2 – n^2 = (n + 1 + n)(n + 1 – n) = 2n + 1