Consecutive Integers Calculator

Name: Consecutive Integers Calculator
Author: Jitendra Kumar

Generate consecutive integer sequences or solve sum word problems for consecutive, even, and odd integers.

Last Updated: May 2026

Sequence

30, 31, 32

Sum

Average

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.

Mode

Sequence type

Count

Number of terms, from 1 to 200.

Target sum

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.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

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Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

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Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

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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.

Keep the research moving with Integer Calculator, Mean Calculator, Long Addition Calculator, and Scientific Calculator.

Frequently Asked Questions

Consecutive integers are whole numbers that follow one another with a difference of 1, such as 6, 7, 8 or -2, -1, 0.

Consecutive even integers and consecutive odd integers follow the same parity and increase by 2, such as 12, 14, 16 or 31, 33, 35.

Choose Solve from sum, enter the count and target sum, then select whether the terms are all integers, even integers, or odd integers.

The target sum must produce an integer first term with the correct parity. If it does not, there is no exact sequence for that setup.

Yes. Consecutive integer sequences can include negative values, zero, and positive values.

It uses last = first + (count - 1) x step and sum = count x (first + last) / 2. The step is 1 for ordinary consecutive integers and 2 for even or odd sequences.