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Consecutive Integers - GCSE Maths Definition

Reviewed by: Jamie Wood

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What are consecutive integers in GCSE maths?

Consecutive integers are whole numbers that follow each other in order, with no numbers missed out.

  • 5 comma space 6 comma space 7 comma space 8 is a sequence of consecutive integers.

  • 2 comma space 4 comma space 6 comma space 8 is not a sequence of consecutive integers.

In the context of GCSE Maths, the phrase "consecutive integers" frequently appears in proof problems. For example "show that the sum of two consecutive integers is always an odd number". For this purpose, consecutive integers can be expressed algebraically in the following ways (where n is an integer).

  • n and n plus 1

  • n minus 1 and n

  • 2 n and 2 n plus 1(this is an even number, and the next consecutive integer).

  • 2 n plus 1 and 2 n plus 2(this is an odd number, and the next consecutive integer).

For a sequence of several consecutive numbers, n, n plus 1, n plus 2, n plus 3, and so on could be used.

Understanding the meaning of consecutive integers is essential for being able to solve many proof and sequences problems.

Consecutive integers revision resources to ace your exams

Save My Exams has a great range of resources to explore consecutive integers and proof in more detail. Try exploring our algebraic proof revision notes and answering our exam questions.

Explore our GCSE Maths revision resources.

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Jamie Wood

Reviewer: Jamie Wood

Expertise: Maths

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

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