Sequence Puzzle

Sequence worksheets where the answer page tells you the rule

Each item is six numbers long. The first four are printed and the last two are blank, so the solver has to work out the rule and then apply it twice — which is a better test than one blank, because applying a rule once can be a lucky guess and applying it twice usually is not.

The four rule families

• Add a constant. Start anywhere from 1 to 20, step from 2 to 9. The easiest family, and the first one everybody tries.
• Multiply by a constant. Doubling or tripling from a start of 1 to 6. These run away quickly: begin at 6, triple, and the sixth term is 1,458.
• Square numbers. Six consecutive squares. The gaps grow, which is the tell.
• Two sequences woven together. Odd positions follow one arithmetic rule and even positions another, with the two starts kept far enough apart that the woven terms never collide and read as a single muddled run instead of two clean ones.

That last family is the one worth the sheet. A solver who has only met "add 3" sequences will hunt for a single step, not find one, and decide the question is broken. Learning to read every other term is a real technique, and it is the bridge from pattern-spotting to algebra.

How many items

Between 6 and 24, defaulting to 12. Twelve is about a fifteen-minute exercise for a competent Year 5 pupil and about a starter task for a secondary class.

The rule family for each item is chosen at random, so a 24-item sheet lands at roughly six of each. There is no way to drill a single family here. For most purposes the mixture is the point anyway, since knowing which question to ask is most of the skill.

The answer page

It gives the two missing terms and names the rule in words: "add 7", "multiply by 3", "square numbers (3², 4², 5², …)", "two interleaved sequences (add 4 and add 2)".

Naming the rule matters when you are marking. A pupil who wrote the right numbers by extending the differences without ever seeing the rule has done something different from one who spotted it, and a rule stated in words gives you the language to have that conversation.

Why sequences are worth the time

Because "what is the rule?" is the question algebra is built on, and it arrives years before the notation does.

A pupil fluent at reading a sequence has already met the idea of a general term, of a constant difference, and of a rule that holds at every position and not only at the next one. So when nth terms turn up on the timetable, that pupil is being handed notation for something they can already do. Much easier than meeting both at once.

Print at 100% on A4 or US Letter. Every sheet is generated fresh; the seed reproduces one exactly.