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MathidiaMathematics Academy
Sequences and patterns
Lesson 41 of 75
Introduction

Continue sequences

Objective. Recognise and continue additive and multiplicative patterns.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A sequence is a list of numbers following a particular pattern, and continuing it means working out the rule linking consecutive terms. An additive sequence changes by a constant amount each time, such as 3, 7, 11, 15, which adds 4 at every step. A multiplicative sequence changes by a constant factor instead, such as 2, 6, 18, 54, which multiplies by 3 each time. Spotting whether the differences or the ratios between terms stay constant tells you which type of sequence you are dealing with, allowing the next terms to be predicted.

Worked example

Find the next two terms of the sequence 5, 9, 13, 17, ...

5 … 9
Illustrated card showing 5 … 9
  1. 1Find the difference between consecutive terms: 9−5=4, 13−9=4.
  2. 2Since the difference is constant at 4, this is an additive sequence.
  3. 3Add 4 to the last given term: 17+4=21.
  4. 4Add 4 again: 21+4=25.

Answer: 21, 25

Concept mastery

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. Pupils sometimes assume every sequence is additive, missing a multiplicative pattern like 1, 3, 9, 27 and wrongly adding a constant difference instead. Check both the differences and the ratios between consecutive terms before deciding.

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