Consecutive Integers Calculator
Generate consecutive integer sequences or solve sum word problems for consecutive, even, and odd integers.
Last Updated: May 2026
Sequence
30, 31, 32
Sum
93
Average
31
First to last
30 to 32
Consecutive Integer Inputs
Generate a sequence from the first term, or solve the first term from a total sum and count.
Number of terms, from 1 to 200.
Total of all terms.
Sequence Setup
| Item | Formula | Value |
|---|---|---|
| Sequence type | consecutive integers | Step size is 1. |
| First term | a | 30 |
| Last term | l | 32 |
| Count | n | 3 |
| Sum formula | n(a + l) / 2 | 3 x (30 + 32) / 2 |
| Range | last - first | 2 |
Terms
| Term | Pattern | Value |
|---|---|---|
| 1 | 30 + 0 | 30 |
| 2 | 30 + 1 | 31 |
| 3 | 30 + 2 | 32 |
Integer Sequence Notice
This calculator is for educational integer sequence problems. It uses exact integer arithmetic, rejects non-integer counts and sums, and reports when a requested count and sum do not form an exact sequence.
Checked by Jitendra Kumar
Consecutive Integers Calculator is checked for formula labels, source links, and result limits.
Jitendra Kumar, Founder & Editorial Standards Lead. Updated May 2026. Scope: math calculators.
How to Use the Consecutive Integers Calculator
Step 1: Choose a mode
Use Solve from sum for word problems, or Generate from first integer when the first term is known.
Step 2: Select the sequence type
Pick consecutive integers, consecutive even integers, or consecutive odd integers.
Step 3: Enter count and value
Enter the number of terms and either the target sum or the first integer.
Step 4: Review the sequence
Use the result cards and tables to check the first term, last term, sum, average, and term pattern.
How Consecutive Integer Problems Work
Consecutive integers increase by 1, so a sequence can be written as x, x + 1, x + 2, and so on. Consecutive even and odd integers increase by 2, so they use x, x + 2, x + 4.
When the first term is known, the calculator builds each term and applies the arithmetic sequence sum formula: sum = count x (first + last) / 2.
When only the count and sum are known, the calculator rearranges the same pattern to solve for the first term, then checks that the result is an integer with the required parity.
Consecutive Integers Guide
Consecutive Integer Formulas
These formulas cover ordinary consecutive integers plus the even and odd variants commonly used in algebra word problems.
| Concept | Formula | Use |
|---|---|---|
| Consecutive integers | n, n + 1, n + 2, ... | Each term increases by 1. |
| Consecutive even integers | n, n + 2, n + 4, ... | Each term increases by 2 and starts even. |
| Consecutive odd integers | n, n + 2, n + 4, ... | Each term increases by 2 and starts odd. |
| Last term | first + (count - 1) x step | Finds the final term in the sequence. |
| Sum | count x (first + last) / 2 | Adds all terms in the consecutive sequence. |
| Solve from sum | first = (sum - step x count(count - 1) / 2) / count | Finds the first term from a target sum. |
Examples
The same structure works for positive, negative, even, and odd integer sequences. The difference is the step size between terms.
| Problem | Setup | Result |
|---|---|---|
| Three consecutive integers sum to 93 | x + (x + 1) + (x + 2) = 93 | 31, 32, 33 |
| Four consecutive odd integers sum to 136 | x + (x + 2) + (x + 4) + (x + 6) = 136 | 31, 33, 35, 37 |
| Five consecutive even integers starting at 12 | 12, 14, 16, 18, 20 | sum = 80 |
| Seven consecutive integers starting at -3 | -3, -2, -1, 0, 1, 2, 3 | sum = 0 |
Mistakes To Avoid
Consecutive integer word problems are usually setup problems. Confirm the step size and parity before solving for the first term.
| Mistake | Fix |
|---|---|
| Using +1 for odd or even sequences | Consecutive odd and even integer sequences step by 2. |
| Forgetting parity | The first term must be even for even sequences and odd for odd sequences. |
| Assuming every sum works | Some count and sum combinations do not produce an integer first term. |
| Dropping negative values | Consecutive integers can cross zero or start below zero. |
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- 1.OpenStax - Elementary Algebra, Use a Problem-Solving Strategy(Accessed May 2026)
- 2.Khan Academy - Sums of Consecutive Integers(Accessed May 2026)
- 3.LibreTexts - Consecutive Integers(Accessed May 2026)