A series of free, online lessons suitable for GCSE Maths, with videos, examples and solutions. These lessons cover quadratic sequences and cubic sequences.

The following figure shows how to derive the formula for the nth term of a quadratic sequence. Scroll down the page for examples and solutions on how to use the formula. The following figure shows how to derive the formula for the nth term of a cubic sequence. Scroll down the page for examples and solutions on how to use the formula. How to find the nth term of a quadratic sequence?

When trying to find the nth term of a quadratic sequence, it will be of the form
an2 + bn + c
where a, b, c always satisfy the following equations
2a = 2nd difference (always constant)
3a + b = 2nd term - 1st term
a + b + c = 1st term

Example:

1. Find the nth term, Tn of this sequence
3, 10, 21, 36, 55, …
2. Find the nth term, Tn of this sequence
0, 7, 20, 39, 64, …

Nth term of a Quadratic Sequence

GCSE Maths revision Exam paper practice

Example:
(a) The nth term of a sequence is n2 - 2n.
Work out the first three terms of the sequence.

(b) Work out the nth term of the sequence 5, 6, 8, 11, 15, …

Linear and Quadratic Nth Terms of Sequences

GCSE Maths revision Exam paper practice and help
AQA Linked Paired Pilot Methods 2 Higher Jan 2012 Question 11

Example:
(a)Work out the nth term of the sequence
6, 11, 16, 21, 21, …

(b) Work out the nth term of the sequence.
9, 15, 23, 33, 45, …

Nth Term of a Quadratic Sequence

Find the nth (general) term of a quadratic sequence by using a method of differences.

Example:
What is the nth term of this quadratic sequence?
2, 17, 40, 71, 110, 157, …

Nth Term of a Cubic Sequence

How to derive the formula for the nth term of a cubic sequence?

Example:
Find nth term of the following cubic sequences
-6, -4, 10, 42, 98, 184, …
17, 59, 143, 287, 509, 827, …

Nth Term of a Cubic Sequence

Find the nth (general) term of a cubic sequence by using a method of differences.

Example:
What is the nth term of this cubic sequence?
0, -12, -52, -132, -264, -460, …

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