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Growing patterns – practice for Years 5–9

Sample questions on Growing patterns with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 5–9
Curriculum area
Problem solving and non-routine tasks

Question types: Growing patterns

Rule: Growing patterns

Find how many squares are added at each step: that number goes in front of n.

The nth pattern = the step × n + what is left to make the number in pattern 1.

Example: 5, 8, 11, … (+3 each time): the nth has 3 × n + 2, pattern 10 has 3 × 10 + 2 = 32

Watch out: Pattern 10 is not 10 times pattern 1. Check the rule on patterns 1 and 2.

Sample questions

  1. Question 1 Easy

    The shapes are made of small squares following a fixed rule. How many squares will the 10th shape have?

    Shape 1Shape 2Shape 3
    Show the solution
    Answer: 23

    How it works: Each new shape has 2 more squares. Shape n has 2n + 3 squares, so 2 × 10 + 3 = 23

  2. Question 2 Normal

    The shapes are made of small squares following a fixed rule. How many squares will the 10th shape have?

    Shape 1Shape 2Shape 3
    Show the solution
    Answer: 22

    How it works: Each new shape has 2 more squares. Shape n has 2n + 2 squares, so 2 × 10 + 2 = 22

  3. Question 3 Hard

    The shapes are made of small squares following a fixed rule. How many squares will the 10th shape have?

    Shape 1Shape 2Shape 3
    Show the solution
    Answer: 31

    How it works: Each new shape has 3 more squares. Shape n has 3n + 1 squares, so 3 × 10 + 1 = 31

Related topics

All Maths topics

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