# How do you find three consecutive odd integers such that four times the middle integer is twice the sum of the other two integers?

##### 1 Answer

Nice question.

Any three consecutive odd integers have this property. (As do any three consecutive even integers.)

To solve this, let the consecutive odd integers be

(We'll throw out any non-odd solutions.)

We want

But

We want:

But for any number,

The question asks only for odd solutions, so:

Any (every) three consecutive odd integers will solve the problem.

**Additional Notes**

We could have used

Or we could make sure they are odd by making the numbers:

Again, every number