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Quadratic Sequences

Deduce expressions to calculate the nth term of quadratic sequences.

Level 1 Level 2 Level 3 Exam-Style Description Help More Sequences

This is level 1; Quadratic sequences of the form n2 + c. You can earn a trophy if you get at least 4 questions correct.

Find the nth term of the sequence:
4, 7, 12, 19, 28, 39, ...Quadratic Sequence


Correct Wrong
Find the nth term of the sequence:
6, 9, 14, 21, 30, 41, ...


Correct Wrong
Find the nth term of the sequence:
11, 14, 19, 26, 35, 46, ...


Correct Wrong
Find the nth term of the sequence:
-12, -9, -4, 3, 12, 23, ...


Correct Wrong
Find the nth term of the sequence:
-10, -7, -2, 5, 14, 25, ...


Correct Wrong

This is Quadratic Sequences level 1. You can also try:
Level 2 Level 3


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


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Description of Levels



Level 1 - Quadratic sequences of the form n2 + c

Level 2 - Quadratic sequences of the form an2 + c

Level 3 - Quadratic sequences of the form an2 + bn + c

Exam Style questions are in the style of GCSE exam paper questions and worked solutions are available for Transum subscribers.

Handshakes - Try this lesson Starter which can generate a quadratic number sequence.


This video explains how to find the nth term of a quadratic sequence and is from Mr Hegarty.

A shorter, concise method is shown here.

Quadratic Sequences Aide Memoire
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.