Does the rule really fit?
1, 2, 4 — what comes next? There is more than one honest answer.
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Step 1 of 4
- The list so far: 1, 2, 4.
- Double each time: the next term is 8.
- Add 1, then 2, then 3: the next term is 7.
- Both fit. The list cannot choose.
The rule
Two rules fit 1, 2, 4. So the next term can be 8 or 7.
Doubling fits 1, 2, 4. The next term is 8. Adding 1, then 2, then 3 fits too. The next term is 7. The two rules agree on three terms and differ at the fourth.
The same happens with 3, 5, 7. The rule "add 2" gives 9 next. A prime has exactly two factors: 1 and itself. The odd primes are the primes except 2: 3, 5, 7, 11. That rule gives 11 next.
Three terms that fit do not prove a rule.
So when a question gives you the rule, use that rule. Do not guess one from the first terms.
| List | Rule one | Next | Rule two | Next |
|---|---|---|---|---|
| 1, 2, 4 | double each time | 8 | add 1, then 2, then 3 | 7 |
| 3, 5, 7 | add 2 each time | 9 | the odd primes | 11 |
Some lists have no simple add or multiply rule. The primes 2, 3, 5, 7, 11, … are such a list.