Four consecutive odd integers add up to 64. What are the numbers?

1 Answer
Apr 26, 2016

13,15,17and19

Explanation:

Let the first odd number be =2n+1, where n is any positive integer.

Thus we have four consecutive odd numbers
(2n+1),(2n+3),(2n+5)and(2n+7)
Setting the sum of these numbers equal to the given value

(2n+1)+(2n+3)+(2n+5)+(2n+7)=64, simplifying
(8n+16)=64, dividing both sides and solving for n
(n+2)=8
or n=82=6
The numbers are
(2×6+1),(2×6+3),(2×6+5)and(2×6+7)
13,15,17and19