Question

Express the given quantity in terms of the indicated variable.

The sum of three consecutive even integers; n = first integer of the three.

Short answer

The integer is $3n+6$.

Step-by-step solution

Step 1. Concept used.

Consecutive integers differ by 2. The numbers 4, 6, and 8 are examples of consecutive integers.

Step 2. Add the expression.

Use this fact to model the first, second, and third integers.

$n,n+2,n+4$

So, add the expressions:

$n+\left(n+2\right)+\left(n+4\right)$

Step 3. Evaluate the expression.

Remove parentheses:

$=n+n+2+n+4$

Add the similar terms:

$=3n+6$