1119 Evaluate each sum that exists. 8. a30 i=1 15i + 22 9. a 5 i=1 1-3 # 2i2 10. a ∞ i=1 12i2 # 4 11. a ∞ i=1 54 a 2 9b i Write the first five terms of each sequence. Determine whether the sequence is arithmetic, geometric, or neither. 1. an = 1-12n1n2 + 22 2. a n = -3 a 1 2b n 3. a1 = 2, a2 = 3, an = an-1 + 2an-2, for n Ú 3 Determine the indicated term for each sequence described. 4. An arithmetic sequence has a1 = 1 and a3 = 25. Find a5. 5. A geometric sequence has a1 = 81 and r = - 2 3 . Find a6. Find the sum of the first ten terms of each series. 6. arithmetic; a1 = -43, d = 12 7. geometric; a1 = 5, r = -2 Write the binomial expansion of each expression. 12. 1x + y26 13. 12x - 3y24 14. Find the third term in the expansion of 1w - 2y26. Evaluate each expression. 15. 8! 16. C110, 22 17. C17, 32 18. P111, 32 19. Let Sn represent the statement, and use mathematical induction to prove that Sn is true for every positive integer n. 1 + 7 + 13 + g+ 16n - 52 = n13n - 22 Solve each problem. 20. Athletic Shoe Styles A shoe manufacturer makes athletic shoes in 4 different styles. Each style comes in 3 different colors, and each color comes in 2 different shades. How many different types of shoes can be made? 21. Seminar Attendees A mortgage company has 10 loan officers: 4 women and 6 men. In how many ways can 4 of these officers be selected to attend a seminar? In how many ways can 2 women and 2 men be selected to attend the seminar? 22. Course Schedule Arrangement A student must select 4 courses from 15 that are offered in a semester. How many different arrangements of the 4 courses are possible? 23. Drawing Cards A card is drawn from a standard deck of 52 cards. Find the following probabilities in parts (a)–(c). (a) A red three is drawn. (b) A card that is not a face card is drawn. (c) A king or a spade is drawn. (d) What are the odds in favor of drawing a face card? Chapter 11 Test CHAPTER 11 Test
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