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Solution Explanation

a b 5, 8, 11, 14, 17 c 5 sticks are required to start the pattern, and an additional 3 sticks are required to make the next term in the pattern.

Now you try

Follow the pattern, by adding three sticks each time to the right-hand side.

Count the number of sticks in each term. Look for a pattern.

a Draw the next two shapes in the spatial pattern shown.

b Write the spatial pattern as a number pattern relating the number of sticks required to make each shape.

Example 20 Finding a general rule for a spatial pattern

a Draw the next two shapes in this spatial pattern.

b Copy and complete the table.

Number of triangles 1 2 3 4 5

Number of sticks required 3 c Describe a rule connecting the number of sticks required to the number of triangles. d Use your rule to predict how many sticks would be required to make 20 triangles. c Describe the pattern by stating how many sticks are required to make the first term, and how many sticks are required to make the next term in the pattern. Continued

Solution Explanation

a Follow the pattern by adding one triangle each time. b c Number of sticks = 3 × number of triangles 3 sticks are required per triangle. d Number of sticks = 3 × 20 = 60

An extra 3 sticks are required to make each new triangle.

∴ 60 sticks are required.

Now you try b Copy and complete the table. number of triangles = 20 so number of sticks = 3 × 20 c Describe a rule connecting the number of sticks required to the number of shapes. d Use your rule to predict how many sticks would be required to make 20 shapes.

Draw the next two shapes in this spatial pattern.

Exercise 2I

FLUENCY b Write the spatial pattern above as a number pattern in regard to the number of sticks required to make each shape.

1 a Draw the next two shapes in the spatial pattern shown.