A number sequence becomes less mysterious when you stop asking “What is the answer?” and first ask “What changed from one number to the next?”
Check the differences
For 7, 12, 17, 22, the difference is +5 every time. If the pattern is not obvious, write the jumps down.
Check multiplication or division
Fast growth often points away from addition. In 3, 6, 12, 24 every term doubles. In 160, 80, 40, 20 every term halves.
Look for alternating rules
Consider 5, 8, 16, 19, 38. The rule is +3, ×2, +3, ×2. Marking each jump separately makes this much easier to see.
Split odd and even positions
If the sequence still looks irregular, read the 1st, 3rd and 5th terms together, then the 2nd, 4th and 6th. Some puzzles interleave two simple patterns.
Watch for changing steps
In 10, 12, 15, 19, 24 the differences are +2, +3, +4 and +5. A changing difference can itself be the pattern.
Do not invent a complicated rule too early
Short number lists can technically fit many formulas. Casual puzzles normally expect a simple repeatable relationship, so test the basic possibilities first.
Practise these ideas in Number Sequence, or read our longer number sequence guide.
A pattern that tricks first impressions
Consider 1, 4, 9, 16, 25. The gaps are +3, +5, +7, +9, so the next gap is +11 and the next number is 36. Calling this a “plus three pattern” after seeing the first two numbers would be premature.
Now try 2, 8, 4, 16, 6, 24. Read odd and even positions separately: 2, 4, 6 and 8, 16, 24. The expected next odd-position term is 8. This is why alternating rules deserve their own check.
One starting number, three very different rules
Compare 2, 4, 6, 8 with 2, 4, 8, 16 and 2, 4, 7, 11. All three start with 2, 4. After that they separate. The first adds two each time. The second doubles. The third adds 2, then 3, then 4, so the next move would be +5. Looking at only the first pair does not give you enough evidence to select a rule confidently.
When a sequence feels irregular, mark the jump between every adjacent pair. If those jumps are constant, you have an addition or subtraction pattern. If they grow in a predictable way, there may be a second pattern hiding inside the differences. If nothing fits, split the sequence into odd and even positions. A surprising number of puzzle-style sequences become simpler when you read them as two separate tracks.
The habit that stops premature answers
Once you have a candidate rule, work backward through the visible terms and check whether it reproduces the line without exceptions. If the rule works only for the last two numbers, keep looking. You can practise this deliberately in Number Sequence: pause before choosing and name the rule in a short sentence. “Each jump increases by one” is much stronger reasoning than “the next number feels like 20.”