Question

Write and simplify an expression to represent the sum of three consecutive odd integers.?

Answer 1

you could write x + x+2 + x+4, but what if x is even?
To make sure we have only odd numbers use
2x+1 + 2x+3 + 2x+5 = 6x+9 = 3(2x+3)

so the sum of 3 consecutive odd numbers is just 3 times the middle one. You can see this more easily if you let the numbers be

x-2 + x + x+2 = 3x

In fact, the sum of any three consecutive terms of an arithmetic sequence is just 3 times the middle term.

Answer 2

This really helped me. Thanks!