Write down the changes
Consider 4, 7, 10, 13. The changes are +3, +3 and +3. If the rule says to keep adding three, the next number is sixteen. Checking the gaps gives a reason for the answer.
Compare 3, 6, 12, 24. The gaps are not constant, but each number is twice the previous one. The next number under that rule is forty-eight. Addition and multiplication describe different changes.
Try it yourself
Write 4, 7, 10, 13. Draw a small arrow between each pair and write “add 3” underneath. The same change works at every step.
Some patterns take turns between two changes. Start at 1 and take turns adding 2, then 5:
- Start at 1. Add 2 to reach 3.
- Add 5 to reach 8.
- Add 2 to reach 10.
- Add 5 to reach 15.
The numbers are 1, 3, 8, 10, 15. To continue, the next change is “add 2”.
Could another rule work?
A short list does not always tell you what must come next. More than one rule can start with the same numbers.
For example, after 2, 4, you might add 2 again to get 6. Or you might double 4 to get 8. You need another clue to choose between those rules.
Read any instructions that come with the puzzle. If it says “keep adding two”, that tells you which rule to use.
Write down each jump
Write the numbers on one line and the changes underneath. Try a simple question: are you adding the same amount each time, or multiplying by the same number?
Check every jump, not just the first one. If the changes take turns, write them in order so you can see which comes next.
Once a rule fits all the steps, use it to work out the next number.