Patterns • Topic 1 of 4

Number Patterns

A number pattern is a list of numbers that follows a rule. The first job is always to find that rule, and the safest way is to look at the difference (or ratio) between each pair of neighbours. If the numbers grow by the same amount every step, the rule is 'add a constant' -- 3, 7, 11, 15 grows by 4 each time, so the next term is 19. If they shrink by the same amount, it is 'subtract a constant' -- 40, 34, 28, 22 falls by 6, so 16 comes next. When the jump itself keeps growing, suspect multiplication: 2, 6, 18, 54 is not adding anything fixed, it is multiplying by 3, so 162 follows. Skip counting (counting in 2s, 5s, 10s) is the simplest growing pattern and the one children meet first. The golden rule for the exam: once you think you have the rule, test it across the whole sequence. If 'add 4' works on the first gap but not the second, your rule is wrong -- a genuine CTET pattern obeys one rule from start to finish.

✅ Solved examples

1. Find the next term: 5, 9, 13, 17, ___
The difference between each pair is 4 (9-5, 13-9, 17-13 all equal 4), so the rule is 'add 4'. Apply it once more: 17 + 4 = 21.
2. Find the next term: 80, 71, 62, 53, ___
Each term is 9 less than the one before (80-71 = 9, 71-62 = 9, 62-53 = 9), so the rule is 'subtract 9'. Next term: 53 - 9 = 44.
3. Find the next term: 3, 6, 12, 24, ___
These are not separated by a constant difference; each term is double the previous one (6 = 3x2, 12 = 6x2, 24 = 12x2). The rule is 'multiply by 2', so the next term is 24 x 2 = 48.
4. What is the rule and the next term: 7, 10, 13, 16, ___?
The rule is 'add 3' (the constant difference between neighbours). Applying it to 16 gives 16 + 3 = 19.

✏️ Practice — try these, take hints as needed

1. Find the next term: 6, 11, 16, 21, ___
Look at the gap between neighbours.
The same number is added each time.
26 (rule: add 5)
2. Find the next term: 100, 90, 80, 70, ___
The list is shrinking.
Each term drops by the same amount.
60 (rule: subtract 10)
3. Find the next term: 1, 3, 9, 27, ___
The differences keep growing, so it is not addition.
Try a constant multiplier.
81 (rule: multiply by 3)
4. Skip counting in 4s starting at 4: 4, 8, 12, 16, ___
Add the same jump each time.
The jump is 4.
20

📝 Topic test — 8 questions

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