What is the sum of the first 45 consecutive odd numbers?

You can use the formula for the sum of an arithmetic series.

Sn = (n/2)[2a + (n - 1)d].....n is the number of terms, a is the first term and d the common difference between terms.

In this question, n = 45, a = 1 (as 1 is the first odd number) and d = 2 (the difference between consecutive odd numbers).

Then, S(45) = (45/2)[2 + 44x2] = (45/2) x 90 = 2025.