Find the sum of the odd integers from 3 to 75

sum-of-odd-integers

#1

Find the sum of the odd integers from 3 to 75.

Answer:

Odd numbers between 3 and 75 would be the sequence:

3,5,7, …, 75

The sum of odd numbers from 1 to n, where n is an odd number, formula is:

1 +3 + …+ 2n-1 = n^2

then,

1 +3+…+ 2(38)-1 = (38)^2

by subtracting 1 from both sides:

3+5+…+ 75 = (38)^2 - 1 = 1444 -1

the sum of the odd numbers between 3 and 75 equals 1443