## InsanelyChaotic 2 years ago WHAT did I do wrong here? :( What is the 9th term of the geometric sequence where a1 = -6 and a6 = -6,144? First term: -6 Ratio: -1024 N= 9

1. InsanelyChaotic

Did I mess up on the ratio part?

2. hartnn

yes :P

3. InsanelyChaotic

LOL let me revise

4. hartnn

can i tell you how can you get it ?

5. InsanelyChaotic

0.000097

6. InsanelyChaotic

-6 divided by (-6144)??

7. timo86m

i did this one for you

8. hartnn

no.... common ratio = next term/ previous term a1 and a6 are not consecutive terms

9. InsanelyChaotic

wait huh??? then what is???

10. timo86m
11. hartnn

you'd find common ratio =r by, an = a1 r^{n-1} here, and only for this, n=6 a1=-6 always an=a6 =-6144

12. InsanelyChaotic

so n = 6 temporarily?

13. hartnn

yes, only to find the value of 'r'

14. InsanelyChaotic

ok:)

15. InsanelyChaotic
16. InsanelyChaotic

huh???????????/ ^

17. hartnn

don't use that.

18. InsanelyChaotic

Oh?

19. hartnn

plug in values in the formula and use other calculator or google.

20. InsanelyChaotic

okay

21. InsanelyChaotic

I don't know how to get this

22. hartnn

what u got after plugging in ?

23. InsanelyChaotic

First term: 625 Ratio: -6144 N= 9

24. InsanelyChaotic

I got numbers that were entirely off

25. InsanelyChaotic

in the 8 millions

26. InsanelyChaotic

8 thousands rather*

27. InsanelyChaotic

= -393,216

28. hartnn

ratio is not -6144 ratio = r is what you have to find

29. InsanelyChaotic

Really?????

30. InsanelyChaotic

ughhhh oh my god

31. hartnn

|dw:1363206281770:dw| did you get this step ?

32. InsanelyChaotic

no

33. hartnn

a1=-6 n=6 an=a6=-6144

34. InsanelyChaotic

ohhhh yes yes!!!

35. InsanelyChaotic

what do i do after the -6144

36. hartnn

you mean you want next step ? or right side of same step ?

37. InsanelyChaotic

the next step please:)

38. InsanelyChaotic

my notes are progressing!!

39. hartnn

|dw:1363206708125:dw| got this ?

40. InsanelyChaotic

-6144/ -6 ?

41. InsanelyChaotic

what is that loop thing?

42. hartnn

on right side ? its 'r' r^5

43. InsanelyChaotic

it looks like a deformed male genital

44. hartnn

lol :P

45. InsanelyChaotic

ohhhhhhhh!!!!!!! R

46. hartnn

yes, r = common ratio

47. InsanelyChaotic

got the step:)

48. hartnn

can you find 'r' from that ?

49. InsanelyChaotic

yes let me try

50. InsanelyChaotic

1024^5 = 1.1258999e+15

51. hartnn

its 1024 =r^5 not 1024^5

52. InsanelyChaotic

huh?

53. hartnn

$$1024 =r^5$$ taking 5th root on both sides, $$\large r= \sqrt[5]{1024}=..?$$

54. InsanelyChaotic

let me see

55. InsanelyChaotic

i dont know

56. hartnn

try this : $$r^5=1024=2^{10} \\ r^5= (2^2)^5 \implies r=2^2=4$$

57. hartnn

got how r=4 ?

58. InsanelyChaotic

yes

59. hartnn

good! so, now we have r=4 a1=-6 n=9 find an ?

60. InsanelyChaotic

no

61. hartnn

you can use that link.... or the formula

62. InsanelyChaotic

okay:) Ratio = 4?

63. hartnn

yes, common ratio = r= 4 is what we found out.

64. InsanelyChaotic

3603000625

65. hartnn

no...what values you put ?

66. hartnn

i got : The 9th term is -393216

67. InsanelyChaotic

I made a few minor errors but i fixed it

68. hartnn

great! any more doubts ?

69. hartnn

phew! this took an hour!

70. InsanelyChaotic

hahahh so so sorry!!!!!!!!!

71. InsanelyChaotic

you are literally THE BEST

72. hartnn

not really, but i'll take the compliment ;) Thanks :D