What is the sum of the first 55 consecutive odd numbers?

Answer 1

The sum_of_a_series = 1/2 x number_in_series x (first_number + last_number)

The first odd number is 2 x 1 - 1 = 1, the 55th odd number is 2 x 55 - 1 = 109

Sum = 1/2 x 55 x (1 + 109)

= 1/2 x 55 x 110

= 552

= 3025

It can be seen that the sum of the first n consecutive odd numbers is always n2:

sum = n/2(1 + (2n - 1))

= n/2(2n)

= n2