Equivalent Expressions and Number Sequences
Primary 6 · Mathematics
Equivalent Expressions and Number Sequences
Lesson 3 of 5
15 min
Let's begin
The houses on Keza's street are numbered 3, 7, 11, __, 19. The number on Keza's gate has fallen off. What number should the painter write? If you can spot the pattern, you can find it.
A sequence is a list of numbers that follow a pattern. Each number is a term. Terms that come one after another are consecutive terms.
If the gap between consecutive terms is always the same, the sequence has a common difference.
14, 17, 20, 23, … (add 3 each time; the next term is 26)
50, 44, 38, 32, … (subtract 6 each time; the next term is 26)
Keza's street: 3, 7, 11, __, 19. The gap is 4, so the missing number is 11 + 4 = 15. Check: 15 + 4 = 19.
3, 9, 27, 81, … (multiply by 3; the next term is 243)
400, 200, 100, 50, … (divide by 2; the next term is 25)
Worked example 1
11, __, __, 32, 39. The last gap is 39 − 32 = 7. Add 7: 11 + 7 = 18, 18 + 7 = 25. Check: 25 + 7 = 32. The missing terms are 18 and 25.
Worked example 2
5, __, __, 20. There are 3 equal jumps from 5 to 20. The total jump is 20 − 5 = 15, so each jump is 15 ÷ 3 = 5. The missing terms are 10 and 15.
Worked example 3
(growing gaps). 2, 5, 10, 17, 26, … The gaps are 3, 5, 7, 9, so the next gap is 11 and the next term is 26 + 11 = 37.
Worked example 4
Three consecutive whole numbers add up to 48. What are they?
The middle number is the average: 48 ÷ 3 = 16. So the numbers are 15, 16 and 17. Check: 15 + 16 + 17 = 48.
Worked example 5
Three consecutive even numbers add up to 42. The middle one is 42 ÷ 3 = 14, so they are 12, 14 and 16.
Tip
Look at the gaps. Same gap: add or subtract. Same multiplier: multiply or divide. Growing gaps: look for a pattern in the gaps themselves.
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