Consecutive Integers in Math: Definition & Examples

Definitionnoun phrase

What are consecutive integers in math?

Consecutive integers are integers that follow each other in order, each 1 more than the one before, such as 7, 8, 9 or −2, −1, 0. In algebra, write them as n, n + 1, n + 2. Consecutive even or consecutive odd integers are 2 apart: n, n + 2, n + 4.

In Spanish: enteros consecutivos
Also called: consecutive numbers, consecutive even integers, consecutive odd integers
Grade level: Algebra 1

Grade 7Grade 8Algebra 1CCSS HSA-CED.A.1SATACTGEDHiSETTABEASVABTEAS

Consecutive Integers in a picture

Consecutive integers step by 1. Consecutive even integers and consecutive odd integers both step by 2, so they are written n, n + 2, n + 4.

Formal definition and notation

Integers a₁, a₂, …, a_k are consecutive when a_i+1 = a_i + 1 for each i. They are consecutive even integers when every a_i is even and a_i+1 = a_i + 2, and consecutive odd integers when every a_i is odd and a_i+1 = a_i + 2. In every case the list is an arithmetic sequence of integers.

Symbol	Read it as	Meaning
n, n + 1, n + 2	n, n plus 1, n plus 2	three consecutive integers
n, n + 2, n + 4	n, n plus 2, n plus 4	three consecutive even integers (n even) or odd integers (n odd)
n − 1, n, n + 1	n minus 1, n, n plus 1	three consecutive integers centered on n, handy when the middle one matters

Key facts

Among any two consecutive integers, one is even and one is odd, so their product is always even.
The sum of 3 consecutive integers is 3n + 3 = 3(n + 1): always 3 times the middle number.
The sum of 2 consecutive integers is always odd: n + (n + 1) = 2n + 1.
With negative numbers, “next” still means one more: after −5 comes −4, not −6.
Divide the total by how many numbers there are to find the middle number fast: 3 consecutive integers adding to 72 have middle number 72 ÷ 3 = 24.

Setting up a consecutive integer problem

n + (n + 1) + (n + 2) = 3n + 3

n: the first (smallest) integer
+1 or +2: step size: 1 for consecutive integers, 2 for consecutive even or odd integers

Odd integers also step by 2, not 1: if n is odd, n + 2 is the next odd integer. Only the choice of n makes the list even or odd.

Consecutive Integers examples, step by step

Example 1: Three consecutive integers with a given sum

Warm-up

The sum of three consecutive integers is 72. Find the integers.

Let them be n, n + 1, n + 2. Then n + (n + 1) + (n + 2) = 72.
Combine: 3n + 3 = 72.
Subtract 3: 3n = 69, so n = 23.
The integers are 23, 24, 25. Check: 23 + 24 + 25 = 72.

Answer: The integers are 23, 24 and 25.

Example 2: Consecutive odd integers

Core

Two consecutive odd integers add to 76. What are they?

Odd integers are 2 apart: let them be n and n + 2.
n + (n + 2) = 76, so 2n + 2 = 76.
2n = 74, so n = 37.
The next odd integer is 37 + 2 = 39. Check: 37 + 39 = 76, and both are odd.

Answer: The integers are 37 and 39.

Example 3: A product of consecutive even integers

Test-style

The product of two consecutive positive even integers is 168. What is the larger integer?

Let the integers be n and n + 2: n(n + 2) = 168.
Expand and set to 0: n² + 2n − 168 = 0.
Factor: (n + 14)(n − 12) = 0, so n = 12 or n = −14.
The integers must be positive, so n = 12 and the larger one is 14. Check: 12 × 14 = 168.

Answer: The larger integer is 14 (the pair is 12 and 14).

Common mistakes

✗ MistakeWriting consecutive odd integers as n, n + 1, n + 3.

✓ InsteadWrite them as n, n + 2, n + 4.

Odd numbers such as 7, 9, 11 are 2 apart. n + 1 would be even. The same form works for even and odd; only n decides which.

✗ MistakeSolving 3n + 3 = 72 and answering “23” when the question asked for the largest integer.

✓ Insteadn = 23 is the smallest, so the largest is n + 2 = 25.

n stands for the first integer. Reread the question and report the one it asks for.

✗ MistakeThe integer after −8 is −9.

✓ InsteadThe integer after −8 is −7.

Consecutive means each is 1 more. On the number line, more means to the right, and −7 is to the right of −8.

Not to be confused with

Consecutive Integersvs.Even number

Even numbers are any multiples of 2. Consecutive even integers are even numbers in an unbroken row, 2 apart: 10, 12, 14 (not 10, 14, 20).

Consecutive Integersvs.Arithmetic sequence

Any list that adds the same amount each time, such as 5, 12, 19. Consecutive integers are the special arithmetic sequence of integers with difference 1.

Consecutive Integersvs.Odd number

Odd numbers are integers of the form 2n + 1. Consecutive odd integers are odd numbers in a row, 2 apart: 13, 15, 17.

Quick check: 3 questions

Question 1 of 3

If n is an odd integer, what is the next consecutive odd integer?

Show answer and explanation

Answer: C. Odd integers are 2 apart, so the next one is n + 2 (for example 9 then 11). n + 1 is the next integer, which is even; 2n + 1 jumps much further; n + 3 is even.

Question 2 of 3

The sum of four consecutive integers is 106. What is the smallest?

Show answer and explanation

Answer: A. n + (n + 1) + (n + 2) + (n + 3) = 4n + 6 = 106, so 4n = 100 and n = 25. The integers are 25, 26, 27, 28. 26 and 28 are other members of the list, and 24 comes from forgetting the 6.

Question 3 of 3

Which list shows three consecutive even integers?

Show answer and explanation

Answer: B. −6, −4, −2 are all even and each is 2 more than the one before. 4, 5, 6 are consecutive integers, not all even; 2, 4, 8 and 6, 8, 12 skip even numbers.

Consecutive Integers: frequently asked questions

How do you write consecutive integers in algebra?

Let the first integer be n. Then consecutive integers are n, n + 1, n + 2, and so on. For consecutive even integers or consecutive odd integers, add 2 each time: n, n + 2, n + 4. Write the equation the problem describes, solve for n, then build the rest of the list from n.

Are consecutive odd integers n, n + 1, n + 3?

No. Consecutive odd integers are n, n + 2, n + 4, the same form as consecutive even integers. Odd numbers like 11, 13, 15 are 2 apart. What makes the list odd is that n itself is odd; adding 2 to an odd number always gives the next odd number.

Can consecutive integers be negative?

Yes. −3, −2, −1 are consecutive integers, and so are −1, 0, 1. Each is 1 more than the one before, moving right on the number line. Word problems sometimes add “positive” to rule out a negative solution, as in a product problem where n = −14 also satisfies the equation.

Practice and tools

Equation SolverCheck your equation for a consecutive integer problem Quadratic Equation SolverSolve product problems like n(n + 2) = 168

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS HSA-CED.A.1

Cite this entry

Effortless Math Team. “Consecutive Integers.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/consecutive-integers/

Flashcard

TermConsecutive Integersn, n + 1, n + 2

DefinitionIntegers in a row, each 1 more than the last: 7, 8, 9. Consecutive even or odd integers step by 2: n, n + 2, n + 4.

Study the full deck

Browse all terms in the Math Dictionary · More algebra terms · Random term

IntegerAn integer is a whole number, its opposite, or zero: the counting numbers, their negatives, and zero. The integers are …, −3, −2, −1, 0, 1, 2, 3, … and go on forever in both directions. Integers have no fractional or decimal part, so 4.5 and 12 are not integers.Number System · Grade 6, Grade 7, Grade 8Arithmetic SequenceAn arithmetic sequence is a list of numbers in which you add the same amount each time to get the next term. That fixed amount is the common difference, d. In 4, 7, 10, 13, … the common difference is 3. The nth term is a_n = a₁ + (n − 1)d.Functions · Grade 8, Algebra 1, Algebra 2Even NumberAn even number is an integer that can be divided by 2 with no remainder, so it can be split into two equal groups or into pairs. Even numbers end in 0, 2, 4, 6 or 8, such as 14, 236 and −10. Zero is even. Every even number can be written as 2n for some integer n.Number System · Grade 2, Grade 3, Grade 4NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Negative NumberA negative number is a number less than zero, written with a minus sign, such as −3, −0.5 or −23. On a number line, negative numbers sit to the left of 0. They describe amounts below a starting point: temperatures below zero, depths below sea level, or money owed. Zero itself is neither negative nor positive.Number System · Grade 6, Grade 7Odd NumberAn odd number is a whole number that cannot be split into two equal groups: dividing it by 2 always leaves a remainder of 1. Odd numbers end in 1, 3, 5, 7 or 9, such as 7, 23 and 409. Every odd number can be written as 2k + 1, one more than a multiple of 2.Number System · Grade 2, Grade 3, Grade 4Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6DifferenceA difference is the result of subtracting one number from another. In 12 − 7 = 5, the difference is 5. It tells how much bigger one number is than another, or how far apart they are on a number line. “The difference of a and b” means a − b, in that order.Operations · Grade 1, Grade 2, Grade 3VariableA variable is a letter or symbol that represents a number or value, usually one that can change or is not yet known. In n + 5 = 12, the variable n is an unknown that equals 7. In A = lw, the variables l and w can take many values. Any letter can be a variable, not just x.Algebra · Grade 6, Grade 7, Grade 8EquationAn equation is a statement that two expressions are equal. It always has an equal sign, such as x + 5 = 12 or 3a = 18. Solving an equation means finding the value of the variable that makes it true: here x = 7 and a = 6. An expression like 4x + 7 has no equal sign, so it is not an equation.Algebra · Grade 6, Grade 7, Grade 8Word ProblemA word problem describes a math situation in everyday language instead of only symbols. To solve one, identify what the problem is asking you to find, translate the words into an expression or equation, solve it, and check that the answer makes sense in the story. It is also called a story problem or a real-world problem.Problem Solving · Grade 3, Grade 4, Grade 5Quadratic EquationA quadratic equation is an equation that can be written in the form ax² + bx + c = 0, where a is not 0. Its graph is a parabola, and it may have zero, one, or two real solutions. You can solve it by factoring, by taking square roots, by completing the square, or with the quadratic formula.Algebra · Algebra 1, Algebra 2Combining Like TermsCombining like terms is simplifying an expression by adding or subtracting the terms that have exactly the same variable part. You add their coefficients and keep the variable part: 3x + 2x = 5x. Constants combine with constants. So 3x + 5 + 2x − 1 simplifies to 5x + 4.Algebra · Grade 6, Grade 7, Algebra 1

Consecutive Integers

What are consecutive integers in math?

Consecutive Integers in a picture

Formal definition and notation

Key facts

Setting up a consecutive integer problem

Consecutive Integers examples, step by step

Example 1: Three consecutive integers with a given sum

Example 2: Consecutive odd integers

Example 3: A product of consecutive even integers

Common mistakes

Not to be confused with

Quick check: 3 questions

Consecutive Integers: frequently asked questions

How do you write consecutive integers in algebra?

Are consecutive odd integers n, n + 1, n + 3?

Can consecutive integers be negative?

Related terms

Practice and tools

Sources

Flashcard

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