## anonymous one year ago Find an equation for the nth term of the arithmetic sequence. a19 = -92, a20 = 6 an = -1856 + 98(n - 1) an = -1856 - 98(n - 1) an = -1856 - 98(n + 1) an = -1856 + 98(n + 1) @dan815 @jim_thompson5910 @mathstudent55 @compassionate @zzr0ck3r

1. jim_thompson5910

First isolate d \[\Large a_{19} + d = a_{20}\] \[\Large -92 + d = 6\] \[\Large d= ???\]

2. anonymous

-86 @jim_thompson5910

3. anonymous

then what do we do? @jim_thompson5910

4. jim_thompson5910

you add 92 to both sides

5. jim_thompson5910

6+92 = ??

6. anonymous

98 @jim_thompson5910

7. jim_thompson5910

so d = 98

8. jim_thompson5910

which is why the answer is |dw:1436316159029:dw|

9. jim_thompson5910

|dw:1436316211464:dw|

10. jim_thompson5910

first term is \[\Large a_1 = -1856\] |dw:1436316259108:dw|

11. jim_thompson5910

common difference is d = 98 we add 98 to each term to get the next term |dw:1436316282925:dw|

12. anonymous

so a is the final answer? @jim_thompson5910

13. jim_thompson5910

yeah

14. jim_thompson5910

|dw:1436316316037:dw|

15. anonymous

can u help me with another one? @jim_thompson5910

16. jim_thompson5910

sure

17. anonymous

Find an equation for the nth term of the arithmetic sequence. -17, -13, -9, -5, ... an = -17 + 4(n + 2) an = -17 x 4(n - 1) an = -17 + 4(n - 1) an = -17 + 4(n + 1)

18. jim_thompson5910

what's the first term?

19. anonymous

i dont know @jim_thompson5910

20. jim_thompson5910

just look at the first number given in the sequence

21. anonymous

-17 @jim_thompson5910

22. jim_thompson5910

yeah

23. jim_thompson5910

what must we add to -17 to get to the next term -13 ?

24. anonymous

4 @jim_thompson5910

25. jim_thompson5910

so d = 4

26. jim_thompson5910

First term \[\Large a_1 = -17\] Common difference \[\Large d = 4\]

27. jim_thompson5910

|dw:1436316606279:dw|

28. anonymous

so the answer would be c? @jim_thompson5910

29. jim_thompson5910

|dw:1436316636005:dw|

30. jim_thompson5910

|dw:1436316659391:dw|

31. jim_thompson5910

yes, c

32. anonymous

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively. an = 1 • (-2)n - 1 an = 1 • 2n an = 1 • (-2)n + 1 an = 1 • 2n - 1 @jim_thompson5910 one more?

33. jim_thompson5910

show me what you have so far

34. anonymous

i dont have anything? i dont know how to do it?

35. anonymous

@jim_thompson5910

36. jim_thompson5910

second term = -2 third term = -2*r = -2r fourth term = (-2r)*r = -2r^2 fifth term = (-2r^2)*r = -2r^3 ------------------------------------------------------- solve for r -2r^3 = 16

37. anonymous

how do i do thta? @jim_thompson5910

38. jim_thompson5910

you need to isolate r try to get r all by itself

39. jim_thompson5910

think to yourself -2 times _________ = 16 what goes in the blank?

40. anonymous

r

41. jim_thompson5910

-2 times _________ = 16 think of a number that goes in the blank

42. anonymous

i got 1.25

43. anonymous

@jim_thompson5910

44. jim_thompson5910

no

45. anonymous

so what is it?

46. jim_thompson5910

47. jim_thompson5910

it shows how to solve equations

48. anonymous

i dont know? im stupid lol @jim_thompson5910

49. jim_thompson5910

50. anonymous

can u show me step by step im more of a visual person @jim_thompson5910

51. jim_thompson5910

for example 2 times x = 10 means x = 5 since 2 times 5 = 10

52. jim_thompson5910

2q = 28 means q = 14 because 2 times 14 = 28

53. jim_thompson5910

you can divide both sides by 2 to isolate the variable

54. anonymous

so then its r^3=-8 @jim_thompson5910

55. jim_thompson5910

very good

56. jim_thompson5910

to undo the cube exponent, we take the cube root of both sides |dw:1436317751492:dw|

57. jim_thompson5910

|dw:1436317761724:dw|

58. anonymous

i got this 1±i√3

59. jim_thompson5910

|dw:1436317773660:dw|

60. jim_thompson5910

only focus on the real solutions

61. jim_thompson5910

|dw:1436317819217:dw|

62. anonymous

63. jim_thompson5910

|dw:1436317839091:dw|

64. jim_thompson5910

yeah it's the only one that fits

65. jim_thompson5910

so a1 has to be 1

66. anonymous

one last one? @jim_thompson5910

67. anonymous

Write the sum using summation notation, assuming the suggested pattern continues. -1 + 2 + 5 + 8 + ... + 44 summation of negative three times n from n equals zero to fifteen summation of the quantity negative one plus three n from n equals zero to fifteen summation of negative three times n from n equals zero to infinity summation of the quantity negative one plus three n from n equals zero to infinity

68. anonymous

@jim_thompson5910 @UsukiDoll