MATH 8 1. PATTERNS & SEQUENCES Which expression can be used to find the nth term in the following arithmetic sequence, where n represents a number’s position in the sequence? Position in Sequence Term A. n + 4 2. 3. NAME___________________________ 1 2 3 4 n 5 9 13 17 ? B. 3n + 4 C. 5n D. 4n + 1 What expression can be used to find the nth term in this sequence? 4, 8, 12, 16, ... Hint: Look at the relationship between the terms in the sequence and their position in the sequence. Position in Sequence 1 2 3 4 ... Value of Term 4 8 12 16 ... n Let n represent the position of a number in the following arithmetic sequence. 1 3 , 1, , 2, ... 2 2 Which expression can be used to find any term in the sequence? F. 2n 4. G. 1 n 2 3 H. n 2 J. 5 n 2 What expression could be used to find the nth term? 4, 7, 10, 13, . . . Position Value of Term 1 4 5. What is the 15th term in this sequence? 6. Look at this sequence of numbers. 2 7 3 10 4 13 ... ... n –4, –6, –8, –10, –12, . . . Does the expression –2(n + 1) show the relationship between any term and n, its position in the sequence? ________________ 7. A sequence of numbers was formed using the rule 2n – 3, where n represents the number’s position in a sequence. Which sequence fits this rule? A. 0, 1, 3, 4, 6, … B. 1, 2, 3, 4, 5, … C. 2, 4, 6, 8, 10, … D. –1, 1, 3, 5, 7, … 8. Let n represent a term’s position in a sequence. Which algebraic expression can be used to find the nth term of this sequence? 4, 12, 24, 40, 60, … A. 2n(n + 1) 9. F. n 0.75 11. 2 3 4 5 n 0.25 0.5 0.75 1.0 1.25 ? G. A. 2 3 4 5 6 , , , , , ... 3 6 9 12 18 B. 1 3 4 5 6 , , , , , ... 3 6 9 12 15 n 4 J. n 15 . H. 4n C. 0, D. 2 3 4 5 , , , , ... 3 6 9 12 2 3 4 5 6 , , , , , ... 3 6 9 12 15 This expression describes a pattern of numbers. n(n – 1) + 4 If n represents a number’s position in the sequence, which pattern of numbers does the expression describe? B. 1, 4, 6, 10, 16,… C. 4, 6, 10, 16, 24, ... D. 4, 10, 18, 28, 40, ... This expression describes a pattern of numbers. 2n + 3 If n represents a number’s position in the sequence, which pattern of numbers does the expression describe? B. 3, 5, 8, 13, 21, … C. 5, 7, 10, 14, 19, ... D. 5, 7, 9, 11, 13, ... This expression describes a pattern of numbers. 2n2 1 If n represents a number’s position in the sequence, which pattern of numbers does the expression describe? A. 20, 21, 22, 23, 24, ... 14. 1 n 1 , where n represents the number’s 3n position in a sequence. Which sequence fits this rule? A. 24, 25, 26, 27, 28, ... 13. D. n² + 3 A sequence of numbers was formed using the rule A. 4, 6, 8, 10, 12, ... 12. C. 4n² In the sequence below, which expression can be used to find the value of the term in the nth position? Position in Sequence Term 10. B. 4n B. 1, 7, 17, 31, 49, … C. 1, 5, 9, 13, 17, ... D. 1, 7, 17, 27, 37, ... A sequence of numbers was formed using the rule n(2n + 1) – 2, where n represents a number’s position in the sequence. Which pattern of numbers does the expression describe? A. 1, 3, 5, 7, 9,… B. 1, 8, 19, 34, 53, ... C. 1, 4, 8, 12, 16, ... D. 1, 7, 17, 31, 50, ... 15. Let n represent the term’s position in the following sequence. Write an expression to represent this sequence. 16. Write an expression to represent the pattern in the table. 17. Write an algebraic expression to describe the pattern. 18. Write an algebraic expression to describe the pattern. 5, 13, 21, 29, 37 …….

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