Question

Which of the following correctly identifies 4 consecutive odd integers where the sum of the middle two integers is equal to 24?

A. 5, 7, 9, 11
B. 7, 9, 11, 13
C. 9, 11, 13, 15
D. 11,13, 15, 17
E. 13, 15, 17, 19

Can you clearly and deeply explain to me, please?

Answer 1

try adding the middle terms ... you will find out.

Answer 2

let n be an odd integer
then n+2 would be the next odd integer
ex (1 1+2 =3 (1,3 they are consecutive)
so the sum 4 consecutive integers would be represented as
n + n+2 +n+4 +n+6
but the sum of the two middle =24
so we take n+2 and n+4 (they add up to 24)
n+2 +n+4=24
2n+6=24
2n=18
n=9
You know what an odd number is :D
so four consecutive odd numbers starting from 9 would be
9,11,13,15

Answer 3

i guess it would be better to take
2n - 3, 2n -1, 2n +1, 2n + 3 instead of n's

Answer 4

right :D

Answer 5

I like that avatar of yours.