There are several different ways to solve this problem, but here we would like to present to you a geometrical approach.
Let's start with the first two terms, i.e "1 + 3": 1 + 3 = 4 which is square of 2.
When we add 5 to that we get 1 + 3 + 5 = 9 and this is square of 3.
And, after adding one more term to the sum, we have 1 + 3 + 5 + 7 = 16 which is square of 4. This keeps going on like that.