Quadratic 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.

• Worksheets to find the Sequence & nth term

  Find the sequence & n^th term
  Find the sequence & n^th term
  Find the n^th term of a sequence with fractions

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, 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, …

• Show Video Lesson

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, …

• Show Video Lesson

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, …

• Show Video Lesson

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, …

• Show Video Lesson

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, …

• Show Video Lesson

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, …

• Show Video Lesson

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.