1048 CHAPTER 11 Further Topics in Algebra 9. Find the first five terms of the sequence an = 31-32n-1. 10. Evaluate a 5 i=1 31-32i-1. Write the first five terms of each sequence. See Example 1. 11. an = 4n + 10 12. an = 6n - 3 13. an = n + 5 n + 4 14. an = n - 7 n - 6 15. an = a 1 3b n1n - 12 16. an = a 1 2b n1n2 17. an = 1-12n12n2 18. a n = 1-12n-11n + 12 19. a n = 4n - 1 n2 + 2 20. an = n2 - 1 n2 + 1 21. an = n3 + 8 n + 2 22. an = n3 + 27 n + 3 Concept Check Decide whether each sequence is finite or infinite. 23. The sequence of days of the week 24. The sequence of pages in a book 25. 1, 2, 3, 4, 5 26. -1, -2, -3, -4, -5 27. 1, 2, 3, 4, 5, c 28. -1, -2, -3, -4, -5, c 29. a1 = 4 an = 4 # an-1, if n Ú 2 30. a1 = 2 a2 = 5 an = an-1 + an-2, if n Ú 3 Find the first four terms of each sequence. See Example 2. 31. a1 = -2 an = an-1 + 3, if n 71 32. a1 = -1 an = an-1 - 4, if n 71 33. a1 = 1 a2 = 1 an = an-1 + an-2, if n Ú 3 (This is the Fibonacci sequence.) 34. a1 = 1 a2 = 3 an = an-1 + an-2, if n Ú 3 (This is the Lucas sequence.) 35. a1 = 2 an = n # an-1, if n 71 36. a1 = -3 an = 2n # an-1, if n 71 Evaluate each series. See Example 4. 37. a 5 i=1 12i + 12 38. a 6 i=1 13i - 22 39. a 4 j=1 j -1 40. a 5 i=1 1i + 12-1 41. a 4 i=1 ii 42. a 4 k=1 1k + 12k 43. a 6 k=1 1-12k # k 44. a 7 i=1 1-12i+1 # i 2 45. a 5 i=2 16 - 3i2 46. a 7 i=3 15i + 22 47. a 3 i=-2 2132i 48. a 2 i=-1 5122i 49. a 5 i=-11i2 - 2i2 50. a 6 i=3 12i2 + 12 51. a 5 i=1 13i - 42 52. a 4 i=1 31-22i - 34 53. a 3 i=11i3 - i2 54. a 4 i=11i4 - i32
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