1Cademy - Solving a Three-Consecutive-Integer Sum Problem with Negative Sum

Learn Before

Consecutive Integers

Example

Solving a Three-Consecutive-Integer Sum Problem with Negative Sum

Apply the seven-step problem-solving strategy to find three consecutive integers when their sum is a negative number.

Problem: Find three consecutive integers whose sum is $-42$ .

Read the problem.
Identify what to find: three consecutive integers.
Name the unknowns using the consecutive-integer pattern: Let $n$ = the first integer, $n + 1$ = the second, and $n + 2$ = the third.
Translate into an equation: The sum of the three integers equals $-42$ :

$n + (n + 1) + (n + 2) = -42$

Solve the equation. Combine the three like terms $n + n + n = 3n$ and the constants $1 + 2 = 3$ :

$3n + 3 = -42$

Subtract $3$ from both sides:

$3n = -45$

Divide both sides by $3$ :

$n = -15$

Find the remaining integers: $n + 1 = -15 + 1 = -14$ and $n + 2 = -15 + 2 = -13$ .

Check: $-15 + (-14) + (-13) \stackrel{?}{=} -42$ → $-42 = -42$ $\checkmark$
Answer: The three consecutive integers are $-15$ , $-14$ , and $-13$ .

This example extends the consecutive-integer technique in two ways. First, it involves three unknowns ( $n$ , $n + 1$ , $n + 2$ ) rather than two, so combining like terms produces the coefficient $3$ instead of $2$ . Second, the target sum is negative, which means the solution yields negative integers — reinforcing that the same algebraic approach works regardless of the sign of the answer.

Updated 2026-04-21

Contributors are:

Who are from:

References

OpenStax Elementary Algebra

Learn Before

Related

Learn After