Question

Find the sum of three consecutive even integers. Let n be the first integer of the three.

Answer 1

The sum of three consecutive even integers where n is the first integer is given by the expression 3n + 6.

Step-by-step explanation:

To find the sum of three consecutive even integers where n is the first integer, we can define the three integers as n, n+2, and n+4. Since these are consecutive even numbers, they will always have a difference of 2 between them. To find the sum of these three integers, we add them together:

• n (the first even integer)
• n+2 (the second even integer)
• n+4 (the third even integer)

The sum of the three even integers would be: n + (n + 2) + (n + 4). Simplifying this expression, we get 3n + 6. Therefore, the sum of three consecutive even integers is 3n + 6.