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Sequence Rules Worksheet

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Sequence Rules Worksheet

A sequence follows a pattern. Find how the terms change, then use the rule to predict what comes next. Show your thinking where you can.

Spot the rule

Look at the change from one term to the next. For an increasing sequence, a positive difference means add; for a decreasing sequence, a negative difference means subtract.

1.A robot moves along this number trail: 6, 10, 14, 18, __, __. What are the next two terms, and what is the term-to-term rule?
2.The temperature readings are 17°C, 14°C, 11°C, 8°C, __. Find the next temperature and write the rule.
3.A game awards points in this sequence: 3, 8, 13, 18, ... Which rule describes it?
  • Start at 3 and add 4 each time
  • Start at 3 and add 5 each time
  • Start at 8 and add 5 each time
  • Start at 3 and multiply by 5 each time

Build and use sequences

The position of a term tells you where it appears: the first term is position 1, the second is position 2, and so on.

Position: 1

Term: 4

Position: 2

Term: 7

Position: 3

Term: 10

Position: 4

Term: 13

Position: 5

Term: ____

Position: 6

Term: ____

4.For the sequence in the table, state the term-to-term rule and write the next term after 19.
5.A tile pattern uses 5 tiles in pattern 1, 9 tiles in pattern 2, and 13 tiles in pattern 3. If the pattern continues, how many tiles will pattern 5 use?
6.Start at 28 and subtract 6 each time. Write the first five terms.

Solve the sequence puzzles

Use the pattern carefully. Check that every step follows the same rule.

7.Fill both gaps in this sequence: 7, __, 17, __, 27. The sequence has a constant difference.
8.A student says that 2, 4, 8, 16, 32 is a sequence that adds the same amount each time. Is the student correct? Explain using the differences.
9.Make your own five-term sequence that starts at 12 and decreases by 3 each time. Write the rule too.

3 printable pages

  • Sequence Rules Worksheet, page 1 of 3: Spot the rule, Build and use sequences

    Page 1

  • Sequence Rules Worksheet, page 2 of 3: Solve the sequence puzzles

    Page 2

  • Sequence Rules Worksheet, page 3 of 3: 9. Make your own five-term sequence that starts at 12 and decreases by 3 each time. Write…

    Page 3

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