# Consecutive Integers Calculator

URL: https://speedycalculator.com/calculators/math/consecutive-integers/
Last updated: 2026-10-30

> The consecutive integers calculator finds n consecutive integers (or consecutive even or odd integers) that add up to, or multiply to, a target number.

## Inputs

- I want
- of how many consecutive integers
- to equal
- and I allow

## Results

- Consecutive integers
- Working

## Formula

```
Sum: x + (x + d) + … = S  ⇒  x = (S − d·n(n−1)/2) ÷ n   (d = 1, or 2 for even/odd)
```

## Explanation

Classic word problems ask for "three consecutive integers whose sum is 72" or "two consecutive odd numbers whose product is 143". Writing the integers as x, x + 1, x + 2 (or x, x + 2, x + 4) turns them into simple equations.

### How to use the Consecutive Integers Calculator

- **I want**
- **of how many consecutive integers**
- **to equal**
- **and I allow**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

For sums the calculator solves the linear equation for the first integer and checks that it is a whole number of the right parity. For products it searches near the n-th root of the target.

## Worked example

Inputs — I want: the sum; of how many consecutive integers: 3; to equal: 72; and I allow: any integers.

Results — **Consecutive integers = 23, 24, 25**; Working = x + (x + 1) + … = 72 → n·x + 1·n(n−1)/2 = S → x = 23.

## Key terms

- **Consecutive integers**: Integers that follow each other in order, each one more than the last.

## FAQ

**What are three consecutive integers that add to 72?**
23, 24 and 25.

**How do I write consecutive odd integers?**
x, x + 2, x + 4 … with x odd.

**Why do some sums have no answer?**
The first integer must be a whole number; e.g. no two consecutive integers add to 10.

**Can the integers be negative?**
Yes – −3, −2, −1 add to −6.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)