Number Patterns
Primary 4 · Mathematics
Number Patterns
Lesson 2 of 4
20 min
Let's begin
Mutesi keeps her savings in a small wooden box. In week 1 she has 200 Frw. Every week after that she adds 150 Frw.
Week 1: 200 Frw. Week 2: 350 Frw. Week 3: 500 Frw ... How much will she have in week 6?
Today you will learn about patterns that grow, or shrink, by the same amount each time.
Mutesi's savings follow a rule: start at 200 and keep adding 150.
In week 6 she has 950 Frw.
A pattern where you add (or subtract) the same number every time is called an arithmetic progression. The number you add is the common difference.
Worked example 1
Find the rule and the next two terms of 7, 11, 15, 19, …
Step 1 Take each term away from the next one: 11 − 7 = 4, 15 − 11 = 4, 19 − 15 = 4.
Step 2 The difference is always 4. The rule is: start at 7, add 4.
Step 3 Next terms: 19 + 4 = 23, 23 + 4 = 27.
Worked example 2
90, 82, 74, 66, …
Each term is 8 less than the one before. The rule is: start at 90, subtract 8. Next terms: 58, 50.
Careful! Look at 2, 4, 8, 16. The first difference is 2, but then 4, then 8. The differences are not the same, so this is not an arithmetic progression. Always check more than one pair of terms.
Pattern A: start at 0, add 4. Pattern B: start at 0, add 8.
| Pattern A | 0 | 4 | 8 | 12 | 16 |
|---|---|---|---|---|---|
| Pattern B | 0 | 8 | 16 | 24 | 32 |
Each term of pattern B is double the term above it in pattern A, because 8 is double 4.
Tip
Subtract neighbours. Take each term away from the next one. If you get the same answer every time, that is the common difference. Add it (or take it away) to continue the pattern.
Work each one in your exercise book first. Then tap Show answer to check.
Write the next two terms: 13, 20, 27, 34, …
Answer: 41, 48. The pattern adds 7 each time.
What is the rule for 5, 17, 29, 41, …?
Answer: Start at 5 and add 12. 17 − 5 = 12, 29 − 17 = 12, 41 − 29 = 12.
Write the next two terms: 100, 91, 82, 73, …
Answer: 64, 55. The pattern subtracts 9 each time.
Is 3, 6, 10, 15 an arithmetic progression?
Answer: No. The differences are 3, 4 and 5, which are not the same.
Mutesi keeps saving 150 Frw every week. How much does she have in week 8?
Answer: 1 250 Frw. Continue: 950, 1 100, 1 250.
What you learned today
Sources and credits
The stories, Rwandan examples, drawings and practice questions were written by Ganzaa.
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