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Number sequences worksheets

Two, six, eighteen, fifty-four — what comes next, and how did you know? These free printable worksheets ask a child to find the rule hiding between the terms and then use it, which is the reasoning that later becomes function rules and algebra.

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Number sequences
Number sequences worksheet — Name the rule, extend it, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The move a child practices here is simple and powerful: look at what changes from one term to the next. A sequence that grows by the same amount each time follows an adding rule; one that grows by the same factor follows a multiplying rule. Naming that change, out loud, is the whole of the reasoning — everything else is applying it.

Why this sheet works

Running the rule backwards is the grade-appropriate jump. Extending a sequence forward is one step of arithmetic; being asked which term reaches eighty-two means holding the rule and stepping through it several times, or seeing the shortcut. That is a different and harder kind of thinking than continuing a pattern.

How this one works

One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.

Number sequences, step by step

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