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Quadratic and Cubic Sequences

Deduce expressions to calculate the nth term of quadratic and cubic sequences.

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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

Working:

Correct Wrong
Find the nth term of the sequence:
9, 12, 17, 24, 33, 44, ...

Working:

Correct Wrong
Find the nth term of the sequence:
12, 15, 20, 27, 36, 47, ...

Working:

Correct Wrong
Find the nth term of the sequence:
-13, -10, -5, 2, 11, 22, ...

Working:

Correct Wrong
Find the nth term of the sequence:
-8, -5, 0, 7, 16, 27, ...

Working:

Correct Wrong
Check

This is Quadratic and Cubic Sequences level 1. You can also try:
Level 2 Level 3 Level 4 Level 5

Instructions

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.

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Answers

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Transum,

Thursday, January 20, 2022

"Have you seen the Leapfrog investigation? It's a challenge to find the minimum number of moves to swap the positions of the blue and green frogs by encouraging them to leap from one lily pad to another. The investigation will reveal a quadratic sequence but can you find the rule for the nth term? The investigation has been cunningly named Leapfrog. Have a look!"

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Description of Levels

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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

Level 4 - Quadratic sequence problem solving

Level 5 - Cubic sequences of the form an3 + bn2 + cn + d

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.

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Quadratic 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

Cubic Sequence

Cubic 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. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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