an 7. a1 = 3, an+1 = 2an - 1 In 3 8. a1 = 4, an+1 an - 45. an n! 1 . 3. 5 . ... 47. an = 9-14 llll Find a formula for the general term an of the sequence, (2n) assuming that the pattern of the first few terms continues. 1 . 3 . 5 . ... 9. (2, 4, 8, 16, ... } 48. an = - 1, 4 , 6 , 8 , n! 11. {2, 7, 12, 17,...} 12. 1-1, 3, - 16 , 25 , . . . ) - 2 8 , - 27 ,...) 13. { 1, - 3, 9, 14. {5, 1, 5, 1, 5, 1,... } 49. If $1000 is invested a after n years the inves (a) Find the first five 15-40 will Determine whether the sequence converges or diverges. (b) Is the sequence co If it converges, find the limit. 50. Find the first 40 terms 15. an = n(n - 1) 16. an = n + 1 3n - 1 an+ 1 = 3 + 5n2 17. an = Vn n + n 2 18. an = and a1 = 11. Do the 1 + Vn this type of sequence. 2n 19. an = n 3n+ 1 20. an = 51. For what values of r 52. (a) If {an } is converge 21. an = (-1)"-in ( - 1 ) " n3 22. an =- n2+ 1 n' + 2n2 + 1 23. an = cos(n/ 2) 24. an = cos(2) (b) A sequence {an} is an+1 = 1/(1 + an) 25. (2n - 1)! ( 2 n + 1 ) ! 26. {arctan 2n} gent, find its limit. 53. Suppose you know tha enten In n all its terms lie betwee 27. 28. e 2 n - 1 In 2n ) the sequence has a lim of the limit? 29. {n?e my 30. {n cost nTry 54-60 1Ill Determine whet 31. a, cos'n 32. an = In(n + 1) - Inn decreasing, or not monoto 2 " 33. an = n sin(1) 34. an = Vn - Vn2 - 1 54. an = 5 0 sin 2n 35. an = 1 - 2 1 36. an = 2n -3 1 + Vn 56. an =- 3n + 4 37. {0, 1, 0, 0, 1, 0, 0, 0, 1,...} ,3 , 2 , 4, 3, 5, 4, 6, .. .) 58. an = ne-" (-3) " 39. an = n ! 40. an = 2 " n! 60. an = n +