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Algebraic Pattern Rules Worksheet
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Algebraic Pattern Rules Worksheet
Use n to represent the term position. Show working where it helps you explain your thinking.
Find the rule
Write each rule using n, then use it to find the requested term.
Position, n
1
2
3
4
5
Term
4
7
10
13
16
1.The sequence 4, 7, 10, 13, 16, … follows a constant-step rule. What is the difference between consecutive terms?
2.Write an algebraic rule for the sequence 4, 7, 10, 13, 16, …, where n is the position number.
3.Use your rule for the sequence 4, 7, 10, 13, 16, … to find the 8th term.
4.Which rule generates the sequence 2, 5, 8, 11, 14, … when n is the position number?
- 3n − 1
- 2n + 1
- 3n + 1
- n + 4
5.For the sequence 6, 11, 16, 21, 26, …, write an algebraic rule using n for the position number.
6.Use your rule for 6, 11, 16, 21, 26, … to calculate the 12th term.
7.Find an algebraic rule for the sequence 2, 6, 10, 14, 18, …, where n is the term position.
8.Use your rule for 2, 6, 10, 14, 18, … to find the 15th term.
Use and explain rules
Remember that the first term is at position n = 1.
9.A sequence is defined by 5n − 3. Write its first five terms, starting with n = 1.
10.Explain how the rule 5n − 3 can be used to find any term in a sequence.
11.A sequence has rule 4n + 2. Another expression, 2(2n + 1), is suggested as a rule for the same sequence. Are the expressions equivalent? Explain briefly.
12.Find the rule for the sequence 5, 9, 13, 17, 21, …, where n is the position number.
13.Use your rule for 5, 9, 13, 17, 21, … to find the 20th term.
14.The sequence 5, 9, 13, 17, 21, … follows a constant-step rule. Which position has a term equal to 101?
15.For the rule 3n + 4, list the first six terms, beginning with n = 1.
16.Check the first six terms you found for 3n + 4. Explain how the term at position n is calculated.
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