Prove the sum of three consecutive is divisible by three, that the sum of 5 consecutive integers is divisible by 5, but the sum of four consecutive integers is not divisible by 4

Proved

Step-by-step explanation:

Solving (a):

Let the numbers be:

Their sum is:

Collect Like Terms

Divide sum by 3.

Hence, this is true because there is no fractional part after the division

Solving (b):

Let the numbers be:

Their sum is:

Collect Like Terms

Divide sum by 5.

Hence, this is true because there is no fractional part after the division

Solving (c):

Let the numbers be:

Their sum is:

Collect Like Terms

Divide sum by 4.

Split

The 1.5 means that the sum can not be divisible by 4