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

1 Answer
Apr 26, 2016

13, 15, 17 and 19

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=8-2=6
The numbers are
(2xx6+1), (2xx6+3), (2xx6+5) and (2xx6+7)
13, 15, 17 and 19