WEEK 4 — Sequences: Arithmetic & Geometric Patterns

 


Welcome to Week 4 of your eight-week maths catch-up plan.
This week is all about recognising patterns in sequences and learning how arithmetic and geometric sequences behave.
Each day has a clear focus, simple explanations, and practice questions to build confidence one step at a time.

The video at the top of the page gives you the full lesson.
Below you’ll find the mind map, the day-by-day breakdown, practice exercises, and a short quiz.

Mind Map – Week 4



DAY 1 — What Is a Sequence?

What to understand

A sequence is a list of numbers that follow a rule.
Each number is called a “term”.

Examples:
5, 8, 11, 14…
100, 90, 80, 70…
3, 6, 12, 24…

Practice

Identify the rule (add or multiply):

  1. 2 → 5 → 8 → 11

  2. 10 → 20 → 40 → 80

  3. 25 → 20 → 15 → 10

  4. 3 → 9 → 27 → 81

DAY 2 — Arithmetic Sequences (Add/Subtract)

What to understand

Arithmetic sequences add (or subtract) the same number each time.
This number is called the difference (d).

Examples:
3, 7, 11, 15 (d = 4)
12, 9, 6, 3 (d = –3)

Practice

Find the difference:

  1. 4 → 10 → 16 → 22

  2. 30 → 27 → 24 → 21

  3. 100 → 95 → 90 → 85

  4. 5 → 15 → 25 → 35

DAY 3 — Arithmetic Term n (Simple Version)

What to understand

To find a later term:
Term n = First term + (n – 1) × difference
But today we keep it simple and focus on the idea.

Practice

Find the next terms:

  1. 5, 8, 11, 14 → next two terms?

  2. 20, 15, 10, 5 → next two terms?

  3. First term = 3, difference = 4 → find term 10

  4. First term = 50, difference = –5 → find term 7

DAY 4 — Geometric Sequences (Multiply/Divide)

What to understand

Geometric sequences multiply (or divide) by the same number.
This number is called the ratio (r).

Examples:
2, 4, 8, 16 (r = 2)
81, 27, 9, 3 (r = 1/3)

Practice

  1. 3 → 6 → 12 → 24 → next two terms

  2. 40 → 20 → 10 → 5 → next two terms

  3. First term = 2, ratio = 3 → find term 5

  4. First term = 100, ratio = 1/2 → find term 4

DAY 5 — Mixed Practice (Revision)

Practice

  1. Identify type: 7 → 14 → 28 → 56

  2. Identify type: 10 → 6 → 2 → –2

  3. Give next two terms: 4, 9, 14, 19…

  4. Give next two terms: 16, 8, 4, 2…

Weekly Quiz — Week 4

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(Paste it under HTML view once your quiz is ready.)

If you're stuck, use the mind map or rewatch the video.

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