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Chapter 6 Practice Test For questions 1 to 5, select the best answer. 1. Which is a recursion f (n) formula for the sequence shown? 12 A f (n) 5 f (n 1) 4 B f (n) 5 4n 2 C f (n) 5 2 (n 1)(4) D f (1) 5 2, 6. Determine the first five terms of each sequence. Graph the sequence and state whether it is arithmetic, geometric, or neither. 8 a) tn 5 9 5n 4 b) f (n) 5 2n2 3n 4 _1 (4) c) f (n) 5 0 2 4 n f (n) 5 f (n 1) 4 2. Which expressions represent the missing terms in the binomial expansion shown? (x y)7 5 x7 7x 6y ■ 35x 4y 3 35x 3y 4 21x2y 5 ■ y7 n1 8 d) tn 5 0.2n 0.8 n4 e) tn 5 __ 2 f) f (n) 5 3(2)n 7. Write an explicit formula and a recursion formula for each sequence. a) 64, 32, 16, 8, … A 21y 5x2, 7yx 6 b) 20, 17, 14, 11, … B 21x 5y 2, 7xy 6 c) 80, 76, 72, 68, … C 21x 5y 2, 7xy 6 d) 4000, 1000, 250, 62.5, … D x 5y 2, xy 6 e) 3, 6, 12, 24, … 3. What is the formula for the general term of an arithmetic sequence with a 5 8 and d 5 2? A tn 5 2 (n 1)(8) B tn 5 8 (n 1)(2) C tn 5 8 (n 1)(2) D tn 5 2 (n 1)(8) 4. What are the first three terms of a geometric sequence with a 5 3 and r 5 2? A 3, 5, 7 __ __ a) 6, 10, 14, 18, … b) 3, 6, 12, 24, … c) 5, 10, 20, 40, … d) 5, 10, 15, 20, … 9. Given the explicit formula, write t15 for each sequence. a) f (n) 5 2(3)n 1 b) tn 5 25n 50 C 3, 6, 12 c) tn 5 10(0.1)2n D 2, 5, 8 d) f (n) 5 geometric? A 9 15 21 27 ... B 1 8 27 64 ... C 64 32 16 8 ... __ 8. Write t11 for each sequence. B 2, 6, 18 5. Which series is neither arithmetic nor __ f) 12 2 , 10 2 , 8 2 , 6 2 , ... 3n _ 4 10. Determine the number of terms in each sequence. a) 5, 8, 11, …, 62 b) 4, 12, 36, …, 19 131 876 D 3 2.7 2.4 2.1 ... 412 MHR • Functions 11 • Chapter 6 Functions 11 CH06.indd 412 6/10/09 4:21:10 PM 11. A new lake is being excavated. One day, 19. In the arrangement of letters shown, 1.6 t of material is removed from the lake bed. On each of 10 days after that, 5% more is removed. starting from the top, proceed to the row below by moving diagonally to the immediate right or left. Determine the number of different paths that will spell the name PASCAL. a) Write the first three excavation amounts as a sequence. P b) Write a recursion formula to represent A the amount removed each day. Use this to determine the amount removed on the fifth day. S C A 12. Determine the specified sum for each L series. a) S10 for 200 100 50 ... b) S18 for 12 5 2 ... 15. Use Pascal’s triangle to help you expand each expression. a) (b 3)5 23. A magic square is an arrangement of numbers in which all rows, columns, and diagonals have the same sum. Using the magic square shown, substitute each number with the corresponding term from the Fibonacci sequence. b) 25 17. Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92. L in the first year and 10% every year after that. How much will it be worth 8 years after it is bought? is 32. Determine the fourth term if the sum of the first four terms is reasoning. A 5 502 492 482 472 ... 22 12 B 5 50 49 48 47 ... 2 1 L 22. A sailboat worth $140 000 depreciates 18% b) (2x 5y)6 18. Which is greater, A or B? Explain your L A and the 14th term is 122. Determine the sum of the first 30 terms. 16. The sum of the first three terms of a series a) 40 L C A 21. In an arithmetic series, the 4th term is 62 14. Determine the sum of each geometric series. 8 4 2 a) _ _ _ ... 6912 81 27 9 b) 5 10 20 ... 2560 L C A every year in a city that experiences a lot of hot, sunny days. What percent of colour will a fence in this city have 6 years after being stained? series. b) 8 24 40 ... 280 C A S 20. A new wood stain loses 6.5% of its colour 13. Determine the sum of each arithmetic a) 120 110 100 ... 250 A S 2 7 6 9 5 1 4 3 8 Show that the sum of the products of the rows is equal to the sum of the products of the columns. Chapter 6 Practice Test • MHR 413 Functions 11 CH06.indd 413 6/10/09 4:21:11 PM