1. $a_1=-1,a_2=1,a_3=3,a_4=5,a_5=7$

3. $a_1={\displaystyle \frac{1}{3}},a_2={\displaystyle \frac{2}{5}},a_3={\displaystyle \frac{3}{7}},a_4={\displaystyle \frac{4}{9}},a_5={\displaystyle \frac{5}{11}}$

5. $a_n=32-2n$

7. 9

9. $n+1$

11. 100

13. ${\displaystyle \frac{1343}{140}}$

15. ${\displaystyle \sum _{k=1}^{50}{\displaystyle \frac{1}{k}}}$

17. Arithmetic; $a_1=11,d=-5$

19. Not arithmetic

21. $a_n=3n$

23. $a_n=x+n-1$

25. $d=2,a_n=2n+1$

27. 352

29. 4020

31. Geometric: $a_1=4,r=-2$

33. Not geometric

35. $a_1=16,r=-{\displaystyle \frac{1}{4}},a_n={\displaystyle \frac{{(-1)}^{n-1}}{4^{n-3}}}$

37. $a_{10}=39,366$

39. $S_{12}={\displaystyle \frac{819}{2}}$

41. ${\displaystyle \frac{3}{4}}$

43. ${\displaystyle \frac{3}{2}}$

47. 792

49. ${(x-3)}^4=x^4-12x^3+54x^2-108x+81$

51. $101,376x^5$

53. 24

55. 5040

57. 120

59. 120

61. 3696

63. 15,120

65. ${\displaystyle \frac{1}{2}}$

67. ${\displaystyle \frac{2}{5}}$

69. ${\displaystyle \frac{15}{28}}$

71. ${\displaystyle \frac{1}{17}}$

73.

1. ${\displaystyle \frac{1}{9}}$

2. ${\displaystyle \frac{4}{9}}$

3. ${\displaystyle \frac{5}{9}}$