DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 5: Sequences and Number Patterns

Sequences and Number Patterns

Move from spotting patterns to explaining rules and predicting future terms.

Junior Maths Book 1 pages 69-767 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 69-76

Generate, describe and extend arithmetic and simple geometric patterns.

AI explanation

The AI teacher shows sequences as repeated operations. Arithmetic sequences use a constant difference; geometric sequences use a constant multiplier.

  1. 1Look at the change from one term to the next.
  2. 2A constant difference suggests an arithmetic sequence.
  3. 3A constant multiplier suggests a geometric sequence.
  4. 4A rule should work for every term, not just the first few.

Animated teaching

See the method

Term cards move through add and multiply machines, then a table connects term number to term value.

7+5
12+5
17+5
22+5
27

Rule first

Students should name the rule before predicting the next term.

Why this method works

  • A sequence rule describes a repeated structure.
  • The common difference is connected to linear growth.
  • A multiplier creates repeated scaling rather than repeated addition.

Common mistakes

  • Guessing the next term without finding the rule.
  • Using addition for a geometric pattern.
  • Finding a rule that works once but not for all terms.
  • Forgetting that a sequence can decrease.

Multiple methods

  • You can describe sequences in words, tables, function machines or term-to-term rules.
  • Arithmetic sequences can be extended by common difference or by a position-to-term rule.
  • Geometric sequences can be checked by division between consecutive terms.

Worked examples

Arithmetic sequence

Find the next two terms: 7, 12, 17, 22, ...

Method: Find the common difference.

  1. 1.12 - 7 = 5.
  2. 2.17 - 12 = 5.
  3. 3.The rule is add 5.
  4. 4.22 + 5 = 27 and 27 + 5 = 32.

Answer: 27, 32

Geometric pattern

Find the next term: 3, 6, 12, 24, ...

Method: Find the multiplier.

  1. 1.6 divided by 3 = 2.
  2. 2.12 divided by 6 = 2.
  3. 3.The rule is multiply by 2.
  4. 4.24 x 2 = 48.

Answer: 48

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

What is the next term? 4, 11, 18, 25, ...

Question 2

What is the rule? 81, 27, 9, 3, ...

Question 3

For the rule 5n + 2, what is the 4th term?

Review prompt

Explain how you decide whether a sequence is arithmetic or geometric.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

A sequence begins 2, 5, 10, 17, 26. The differences are 3, 5, 7, 9. Predict the next term and explain your reasoning.

Hint: Look at the pattern in the differences.