If 𝑛𝑛 represents an odd integer, write expressions in terms of 𝑛𝑛 that represent the next three consecutive odd integers. If the four consecutive odd integers have a sum of 56, find the numbers.

Question

I cannot figure this out for the life of me!

Answer 1

Examples of consecutive odd integers are 5, 7, 9 OR 35, 37, 39, 41. Notice that they are 2 apart.

So, if N represents the 1st of consecutive odd integers, the next is N + 2. The 3rd would be 2 more than that or N + 4. Finally the 4th would be N + 6.

The sum of those consecutive odd integers would be:

N + (N+2) + (N+4) + (N+6).

Since you are told their sum is 56 you can write this equation to model that scenario:

N + N + 2 + N + 4 + N + 6 = 56

4N + 12 = 56

4N = 44

N = 11

If this result was not odd then there would not be any such set of consecutive odd integers with a sum of 56.

So the consecutive odd integers is:

11, 13, 15, 17 (add them up to confirm the sum is 56).