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Patterns to Equations
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Patterns to Equations
Use n to represent the term position, starting at n = 1. Show working where needed. For money, use NZ dollars.
Spot and describe patterns
1.The sequence 9, 14, 19, 24, 29, … increases by the same amount each time. What is the common difference, and what rule generates the next term?
2.A sequence starts at 6 and increases by 4 each term. Complete the table for term positions 1 to 5.
Term position n
1
2
3
4
5
Term value
3.Which sequence has a common difference of 6?
- 4, 9, 14, 19, …
- 2, 8, 14, 20, …
- 11, 16, 21, 26, …
- 30, 25, 20, 15, …
Write expressions for sequences
4.A sequence has term rule 7n. Find the value of the fourth term and explain how you evaluated the rule.
5.Write an expression for the nth term of 3, 6, 9, 12, 15, …
6.Match each sequence to its nth-term expression.
- 5, 10, 15, 20, …
- 2, 5, 8, 11, …
- 8, 16, 24, 32, …
- 4, 7, 10, 13, …
- 1, 4, 7, 10, …
- 3n − 1
- 8n
- 3n + 1
- 3n − 2
- 5n
7.For the sequence 6, 10, 14, 18, …, write an expression for the nth term, then use it to find term 9.
Represent patterns with equations
8.The sequence 12, 9, 6, 3, 0, … goes down by a constant amount. State the common difference and write an equation for term value T at position n.
9.A sequence follows T = 4n + 3. Find the first three term values and state whether the sequence increases or decreases.
10.Select every equation that gives a decreasing sequence as n increases.
- T = 18 − 2n
- T = 5n − 1
- T = 30 − 4n
- T = 2n + 7
Use equations in situations
11.Manaia has $12 saved and puts aside another $5 each week. Write an equation for her total M after n weeks, then calculate the total after 8 weeks.
12.A 26 cm ribbon is cut down by 3 cm each time a piece is removed. Write an equation for the remaining length L after n cuts, then find the length after 5 cuts.
13.For the rule T = 2n + 5, list the first five terms, give the common difference, and identify the first term.
14.Explain the difference between an algebraic expression and an equation. Include one example of each.
3 printable pages
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