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More Lessons for GCSE Maths

Math Worksheets

Examples, solutions, videos, games, activities and worksheets that are suitable for GCSE 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:

1. Find the nth term, T_{n} of this sequence

3, 10, 21, 36, 55, ...

2. 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, ...

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

More Lessons for GCSE Maths

Math Worksheets

Examples, solutions, videos, games, activities and worksheets that are suitable for GCSE 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.

When trying to find the nth term of a quadratic sequence, it will be of the form

an

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, T

3, 10, 21, 36, 55, ...

2. Find the nth term, T

0, 7, 20, 39, 64, ...

GCSE Maths revision Exam paper practice

Example:

(a) The nth term of a sequence is n

Work out the first three terms of the sequence.

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

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, ...

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, ...

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, ...

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, ...

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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

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