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The Nth Term of a Quadratic Sequence

The Nth Term of a Quadratic Sequence

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Difference table for the sequence 7, 15, 27, 43 showing first differences +8, +12, +16 and constant second differences +4, +4

A sequence is a list of numbers following a rule, and the position of each term is called the term number nnn. The nth term is a formula that gives the value of a term for any chosen position.

Linear sequences have constant first differences, but quadratic sequences have constant second differences. In the diagram, the gaps between the gaps stay the same, so the sequence is quadratic.

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Practice questions

Question 1

3 marks

Write down the next two terms in the following quadratic sequence.

9 13 19 27

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How is a quadratic sequence identified from its differences?

The Nth Term of a Quadratic Sequence Revision Guide

  1. GCSE
  2. /Maths
  3. /The Nth Term of a Quadratic Sequence

Revision notes for WJEC GCSE Maths The Nth Term of a Quadratic Sequence: explanations and worked examples.

Practise questions

1 of 5

The nth term of a sequence is 2n2+3n−12n^2 + 3n - 12n2+3n−1. What is the 5th term?