A rule, not a guess
5, 8, 11 sit on a board. What comes after 11?
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Step 1 of 4
- The list: 5, 8, 11. Bus tickets: 42, 57, 61.
- The list: the gaps are +3 and +3.
- The tickets: the gaps are +15, then +4.
- One gap repeats every time. The other does not.
The rule
Next comes 14. Each number is 3 more than the one before.
A sequence is a list of numbers in a set order. Each number is a term.
We write the terms t₁, t₂, t₃ and so on. In 5, 8, 11, 14: t₁ = 5 and t₃ = 11.
The small number is the position. So t₃ is the third term.
A list can stop, or go on for ever. Three dots (…) mean it goes on.
A join — where one term meets the next. A rule must fit every join.
The rule "add 3" fits 5, 8, 11. Both joins add 3. So 14 is next.
| The list | The rule to test | Fits every join? |
|---|---|---|
| 5, 8, 11 | add 3 | yes — 3, then 3 |
| 2, 6, 18 | multiply by 3 | yes — ×3, then ×3 |
| 9, 4, 15 | add or multiply | no — gaps are −5, then +11 |