The sum of 4 consecutive odd integers is 104. Find the integers.

Question

If you could explain the steps it would help a lot.

Answer 1

If n is any integer, if we double it it will for sure be even, so 2n is even, then since the number after an even number is an odd number, we can guarantee that 2n+1 will be ODD.

So, if our first odd integer is 2n+1, the 2nd will be 2n+3, the third will be 2n+5, and the fourth odd integer will be 2n+7.

Because these four consecutive odd integers are supposed to sum to 104, we will add them all together.

2n+1 + 2n+3 + 2n+5 + 2n+7 = 104

Combine "like" terms (all of the n's together, and all of the constants together)

8n + 16 = 104

Subtract 16 from both sides

8n = 88

Divide both sides by 8

n=11

11 is NOT the answer, remember our first odd integer was 2n+1, so substituting n=11 into 2n+1, we find that the first odd integer we need is 2(11)+1 = 23

Now let's check: 23 + 25 + 27 + 29 =104 √ works!

So the answer is the integers 23, 25, 27, 29

Answer 2

Four consecutive odd integers:

n

n + 2

n + 4

n + 6

The sum of four consecutive integers

4n + 12

4n + 12 = 102

Can you solve for n and answer?