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

**Related Pages**

Number Sequences

Arithmetic Sequences

Geometric Sequences

Lessons for GCSE/IGCSE Maths

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

an^{2} + 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:**

- Find the nth term, T
_{n}of this sequence

3, 10, 21, 36, 55, … - Find the nth term, T
_{n}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 n^{2} - 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, …

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.