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Number Pattern Rules
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Number Pattern Rules
Complete each pattern and show your thinking where space is provided.
Recognising and continuing patterns
1.The sequence 6, 10, 14, 18, 22, … follows a constant-step rule. State the starting term and the amount added each time.
2.Begin with 4 and add 6 each time. Fill in the four missing terms: 4, , , , , 34.
3.Which instruction produces the sequence 20, 16, 12, 8, 4?
- Begin at 20 and add 4 each time.
- Begin at 20 and subtract 4 each time.
- Begin at 20 and multiply by 4 each time.
- Begin at 20 and divide by 4 each time.
4.Write the first five terms of the pattern that starts at 9 and increases by 7 each time.
Tables and growing patterns
5.A sequence begins at 8 and goes up by 5 each time. Complete the table of term values for positions 1 to 5.
Position n
1
2
3
4
5
Term
8
6.A row of tiles grows like this: Step 1 has 2 tiles, Step 2 has 5 tiles, and Step 3 has 8 tiles. How many tiles will Step 6 have, and what is the rule?
Position rules and algebra
7.For the sequence 3, 7, 11, 15, …, the term rule is 3 + 4(n − 1), where n is the position. Use the rule to calculate the 9th term.
8.A pattern starts at 5 and increases by 8 each time. Write an algebraic rule for the term at position n.
9.A bicycle hire shop charges a $12 sign-up fee and $9 for each day of hire. Write the total cost for 1 to 5 days as a sequence, give a rule using d for the number of days, and calculate the cost for 7 days.
2 printable pages
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