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Patterns to Algebra

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Patterns to Algebra

Use n for the term number unless a question says otherwise. Show working where it helps explain your answer.

Spotting and describing patterns

1.The sequence is 8, 12, 16, 20, 24, … What is the constant difference, and what are the next two terms?

2.Which rule generates the sequence 7, 14, 21, 28, …?

Add 5 each time
Add 7 each time
Multiply by 2 each time
Add 14 each time

3.Select every sequence below that has a constant difference.

5, 9, 13, 17, …
2, 6, 18, 54, …
11, 8, 5, 2, …
1, 4, 9, 16, …

Writing rules with algebra

4.A sequence begins 9, 13, 17, 21, … Write its constant difference and a rule for its nth term. Then use your rule to find the 5th term.

5.Match each sequence to its nth-term rule. In each sequence, the first number is term 1.

A. 3, 6, 9, 12, …
B. 4, 9, 14, 19, …
C. 5, 10, 15, 20, …
D. 2, 7, 12, 17, …

2. 3n
3. 5n − 1
5. 5n − 3
1. 5n − 2
4. 5n

6.A sequence has first term 6 and increases by 3 each time. Write its first five terms and an nth-term rule, where n = 1 for the first term.

Using algebraic expressions

7.For the rule 4n + 3, calculate the 2nd term, the 8th term and the 12th term.

8.A student says the 7th term for the rule 2n + 6 is 20. Substitute n = 7 to check the claim. Is the student correct?

9.At an orchard, Arjun packs apples into boxes. Each box holds 6 apples, and he has 4 extra apples. Write an expression for the total number of apples in n full boxes and find the total when n = 9.

Patterns in context

10.Charlotte starts with $12 in an orchard-stall savings tin and adds $5 each week. Let n be the number of weeks. Complete the totals for weeks 1, 2 and 3, write an expression for the total after n weeks, and calculate the total after 10 weeks.

11.In the expression 7n − 2, what does the variable n represent?

12.The first four terms of a pattern are 3, 6, 9 and 12. Draw a row of groups or shapes that shows how the amount grows from one term to the next. Then write the nth-term rule, taking the first amount as term 1.