4.1 Make sure that you understand what each row means. The first row has been written out in full to help you. Use your calculator to check the numbers in the remaining rows. Did your calculator manage to display the answer to 1 0014?
4.2 What do you notice about the numbers in the table as you look down each column?
4.3 Copy the table above, add three more rows and complete the patterns without using a calculator.
5 Karen uses matches to build the pattern shown below in stages:
Her pattern consists of hexagons that get bigger every time. For each new hexagon, she uses an extra match for each side of the hexagon.
5.1 Copy and complete the table below: Hexagon number
Number of matches
1 6
2 12
5.2 Work out the rule for the number of matches that Karen will use to make the nth hexagon.
5.3 Use your rule in Question 5.2 to calculate the number of matches that Karen will use to make the 20th hexagon.
6.1 Explain in your own words what a recursive pattern is. 6.2 Create your own recursive number pattern by writing down the first two terms and then giving the rule in words for finding each successive term. Swap your book with a partner and ask him or her to write down the next three terms in your pattern.
Challenge
1 Work out the rule for the nth term of this pattern: 2; 4; 8; 16; … . 2 Use your answer to Question 1 to work out the rule for the nth term of this pattern: 6; 12; 24; 48; … .
3 Now work out the rule for the nth term of this pattern: 16; 8; 4; 2; … . 3 4 5
Unit 2: The general rule
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