Question

Express the given quantity in terms of the indicated variable.

The sum of three consecutive integers; n = middle integer of the three

Short answer

The integer is$3n$.

Step-by-step solution

Step 1. Concept used.

Consecutive integers differ by 1. The numbers 3, 4, and 5 are examples of consecutive integers.

Step 2. Add the expression.

Here, note that the first integer is less than the second while the third integer is 1 more than the second

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

$n-1,n,n+1$

So, add the expressions:

$\left(n-1\right)+n+\left(n+1\right)$

Step 3. Evaluate the expression.

Remove parentheses:

$=n-1+n+n+1$

Add the similar terms:

$=3n$