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.
Tips
- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.
Common mistakes to avoid
- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.
Formula
Sum: x + (x + d) + … = S ⇒ x = (S − d·n(n−1)/2) ÷ n (d = 1, or 2 for even/odd)
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.
Frequently asked questions
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.
What formula does the Consecutive Integers Calculator use?
Sum: x + (x + d) + … = S ⇒ x = (S − d·n(n−1)/2) ÷ n (d = 1, or 2 for even/odd).