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AQA GCSE Maths Quadratic sequences

Quadratic sequences

This page covers the following topics:

1. Basics of quadratic sequences
2. Generating terms in quadratic sequences
3. nth term of quadratic sequences

A quadratic sequence is an ordered list of n numbers in which the difference in the first difference between consecutive terms, that is the second difference between terms, is constant. Therefore, a quadratic sequence can be described by formula:

Basics of quadratic sequences

The term to term rule of a quadratic sequence describes how to get from one term to the next in the sequence. To find the term to term rule, identify the common second difference term between consecutive terms. From the term to term rule and the first term of the sequence the position to term rule, or general rule, of a quadratic sequence can be worked out with the formula:

Generating terms in quadratic sequences

The general rule of a quadratic sequence can be used to work out the nth term of the sequence, the term at position n, and is given by the formula:

nth term of quadratic sequences

1

Given the quadratic sequence {Un} = {4, 9, 16, 25, 36, …, Un}, calculate the seventeenth term of the sequence.

Given the quadratic sequence {Un} = {4, 9, 16, 25, 36, …, Un}, calculate the seventeenth term of the sequence.

2

Compute the first five terms of the sequence Un = nΒ² + 27n βˆ’ 184.

Compute the first five terms of the sequence Un = nΒ² + 27n βˆ’ 184.

3

Given a quadratic sequence with a second common difference term 2a = 6 and terms Uβ‚‚ = 14 and U₃ = 30, find U₁ for the sequence.

Given a quadratic sequence with a second common difference term 2a = 6 and terms Uβ‚‚ = 14 and U₃ = 30, find U₁ for the sequence.

4

Given the quadratic sequence Un = 7nΒ² + 14n βˆ’ 3, calculate the seventh term of the sequence.

Given the quadratic sequence Un = 7nΒ² + 14n βˆ’ 3, calculate the seventh term of the sequence.

5

Find the next term in the sequence in the quadratic sequence {3, 12, 27, 48, 75}.

Find the next term in the sequence in the quadratic sequence {3, 12, 27, 48, 75}.

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