Is the sum of two consecutive odd numbers is always divisble by 4?

Answer 1

Yes.

Let the two consecutive odd numbers be (2n - 1) and (2n + 1) for all values of integer n (ie n ∈ ℤ)

Then their sum is:

sum = (2n - 1) + (2n + 1)

= 2n + 2n

= (2 + 2)n

= 4n

= a multiple of 4, so is divisible by 4.