Math PicnicFree printable practice

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.

Customize Practice Save as PDF New questions

Kid stuck on one? You don’t just get the sheet.

See it worked step by step →Answer it on screen →
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 practises 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 this sheet, worked through a step at a time.

Here are the first four terms of a number sequence. 4 9 14 19

491419
4+10 × 5=54
4+10 × 5=54
(104 − 4)÷5=20
term21
  1. Both questions are the same rule read in opposite directions, so find the rule once. 4 to 9 is + 5, and it holds all the way along.
  2. What is the 11th term? Counting on would work and would stop working at the 80th term. From the 4 there are 10 steps to take: 4 + 10 × 5 = 54.
  3. Which term is 104? Same rule, undone: how many steps from 4 up to 104? 104 − 4 = 100, and 100 ÷ 5 = 20 steps — so it is term 21.

Pick another skill