Free printable worksheet

Patterns and Sequences Worksheet

Twenty arithmetic, geometric, alternating, and growing-difference patterns.

Elementary MathGrades 2-53 pagesAnswer key included

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What this worksheet includes

  • Twenty arithmetic, geometric, alternating, and growing-difference patterns.
  • 3-page printable PDF with a complete answer key
  • Designed for Grades 2-5 elementary math practice
  • Available as an immediate free download with no email required

How to use it

Use this patterns and sequences worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.

After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.

Who this practice is for

This resource is designed for grades 2-5 students working on elementary math. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.

Looking for a broader sequence? Browse all Elementary Math worksheets.

Topic guide

How to approach patterns and sequences

A sequence follows a rule from one term to the next. Arithmetic patterns add or subtract a constant amount, while other patterns may multiply, alternate, or use position-based rules.

Compare consecutive terms before predicting. A valid rule must explain every displayed transition, not only the final pair.

Learning objectives

  • Identify sequence rules
  • Extend numerical and visual patterns
  • Find missing terms

Skills to review first

  • Addition and subtraction
  • Multiplication facts
  • Comparing consecutive values
Worked example

Follow the reasoning step by step

Continue 5, 9, 13, ___, ___.

  1. Find 9 − 5 = 4.
  2. Confirm 13 − 9 = 4.
  3. Add 4 to 13 to get 17.
  4. Add 4 again to get 21.

Solution: 17, 21; the rule is add 4.

Try before downloading

Three sample problems

Work each problem, then open the answer to check your result.

Problem 1 · multiplicative pattern

3, 6, 12, 24, ___

Show answer

48

Problem 2 · decreasing pattern

40, 35, 30, ___

Show answer

25

Problem 3 · missing term

2, 5, 8, ___, 14

Show answer

11

Error check

Common mistakes to watch for

  • Using a rule that fits only one step
  • Changing between addition and multiplication without evidence
  • Counting positions as terms