Consecutive integers can be defined as x, x + 1, x + 2, x + 3, etc., where x is an integer.
Consecutive even integers can be defined as x, x + 2, x + 4, x + 6, etc., where x is an even integer.
In your first problem, first define your numbers.
Let x = 1st even number
Let x + 2 = 2nd even number
Let x + 4 = 3rd even number
Let x + 6 = 4th even number
Now add them to obtain the desired sum.
x + x + 2 + x + 4 + x + 6 = 1172
Solve for x, and then determine the 2nd, 3rd and 4th even numbers.
The second part of your question is vague. There are no 5 consecutive even integers that add up to 1172.
x + x + 2 + x + 4 + x + 6 + x + 8 =1172
In the above equation, x is not an integer.