helpmeplz311 3 years ago How to Work out the nth term in the sequences below? http://s1274.beta.photobucket.com/user/hmp311/media/7778AD32-3261-48EB-BA9D-119F07AA70C8-1004-00000419CAFB720A_zpsaf8eeb58.jpg.html?sort=3&o=0 Note: I keep asking this and I get a formula: nth term = dn + (a - d)

1. helpmeplz311

@lgbasallote @nincompoop

2. helpmeplz311

3. lgbasallote

what exactly are you asking?

4. lgbasallote

sequence of what?

5. helpmeplz311

I dont undersyand how to create a formula.

6. helpmeplz311

The worksheet is at the link above.

7. lgbasallote

i see many sequences

8. helpmeplz311

It says you have to work out the terms asked for, create a formula.

9. helpmeplz311

Actually,all of them. I uave to turn this in today.

10. lgbasallote

well...the formula for arithmetic sequence is what you say \[\huge a_n = a_1 + (n-1)d\] where: an is the last term a1 is the first term n is the number of terms d is the common difference

11. helpmeplz311

Please know I am in eight grade.

12. lgbasallote

for example 1, 9, 17, 25, 33,... find the 50th term an would be a50 because a50 is the last term a1 will be 1 because it's the first term n would be 50 because you're looking for the 50th term so you have 50 terms d would be 8 because it adds 8 each number (1 + 8 = 9; 9 + 8 = 17; etc) so if you substitute.. \[\huge a_{50} = 1 + (50 - 1)8\] \[\huge a_{50} = 1 + 49 (8)\] \[\huge a_{50 } = 1 + 392\] \[\huge a_{50} = 393\] so the 50th term is 393 in my example

13. lgbasallote

if you're old enough to learn sequences then you're old enough to learn this

14. helpmeplz311

15. helpmeplz311

may i try o e?

16. lgbasallote

sure

17. helpmeplz311

From my homework.

18. helpmeplz311

ill write in othere first amd then type it on here.

19. lgbasallote

sure

20. helpmeplz311

a44=8+(5-1)9

21. helpmeplz311

number 7

22. helpmeplz311

is that correct?

23. lgbasallote

let me check...

24. helpmeplz311

ok

25. lgbasallote

number 7 is looking for the 50th term not the 44th

26. helpmeplz311

You said a1 was the last term,which in this case is 44

27. lgbasallote

i think you're confused... 8, 17, 26, 35, 44, .... this doesn't mean 44 is the last term "..." means the sequence continues 8, 17, 26, 35, 44, 53, 62, 71 and so on

28. lgbasallote

that means the last term is the 50th term because that's what you're looking for make sense?

29. helpmeplz311

ohhhh

30. helpmeplz311

well, if we erased the 44, would it be correct?

31. lgbasallote

nope. you used 5 as your n

32. helpmeplz311

im sorry.

33. lgbasallote

like i said, the sequence doesn't stop at 44 so there are more than 5 terms

34. lgbasallote

since you're looking for the 50th term, there would be 50 terms make sense?

35. helpmeplz311

yes

36. lgbasallote

good. so rewrite your solution

37. helpmeplz311

wait it shouldve been 50 right

38. helpmeplz311

a50=8+(50-1)9

39. lgbasallote

right. now solve it

40. helpmeplz311

thatll give me the 50th term?

41. helpmeplz311

do you solve for a in the a50?

42. lgbasallote

no... a50 means \(a _{50}\) that means 50th term

43. lgbasallote

just solve the right side

44. helpmeplz311

-2?

45. helpmeplz311

n

46. helpmeplz311

no

47. lgbasallote

how'd you get -2?

48. helpmeplz311

umm,let me tru again

49. helpmeplz311

web2.0calc

50. helpmeplz311

ooo the a50 doesnt matter when solving

51. lgbasallote

yes

52. helpmeplz311

513?

53. helpmeplz311

i lost connection

54. helpmeplz311

back,

55. helpmeplz311

was i right?

56. lgbasallote

you solved 8 + (50-1)9 right?

57. helpmeplz311

yes

58. lgbasallote

did you use a calculator?

59. helpmeplz311

yes i was supposed to use order of operations?

60. lgbasallote

i see what you did (8 + 50 - 1)* 9

61. lgbasallote

that is wrong

62. helpmeplz311

*sigh* ok

63. lgbasallote

you have to do (50 -1) then multiply it to 9 then add 8

64. helpmeplz311

order of ops.

65. lgbasallote

PEMDAS PARENTHESIS expoent MULTIPLICATION division ADDITION subtraction did you forget this?

66. helpmeplz311

no, thats what order of operations is

67. lgbasallote

parenthesis is (50 - 1) multiplication is (50-1)*9 addition is 8 + (50-1)*9

68. lgbasallote

that means you do 50 - 1 first

69. helpmeplz311

o. so, i use that formula, substitute,and solve right side?

70. lgbasallote

yes

71. helpmeplz311

THANK YOU

72. lgbasallote

welcome

73. helpmeplz311

hi amistre

74. lgbasallote

i hope im not in trouble @amistre64

75. amistre64

finally got to the end of it :) howdy!

76. helpmeplz311

howdy,sir

77. helpmeplz311

you mean the end of my endless question?

78. amistre64

i havent seen the links yet, but lgbas stuff looks good so far yeah, these things can get rather lengthy, but thats the way we like to see them. lots of interaction and studying instead of rote answers

79. helpmeplz311

am i in trouble

80. amistre64

lol, not that i can see :) as long as your trying to learn that material you are fine

81. helpmeplz311

yes imam.

82. amistre64

they all look to be arithmetic progressions, so you can apply the same techniques to all of them

83. lgbasallote

i'd like to know though @amistre64 do you know what dn + (a-d) means?

84. lgbasallote

it looks like the formula for arithmetic progression....but it looks weird

85. amistre64

its another way to express the sequence but for n starting at 0 i believe

86. helpmeplz311

amistre can i fan u

87. lgbasallote

dn looks really weird

88. amistre64

dn + (a-d) dn - d + a d(n-1) + a

89. amistre64

you can fan whomever you wish

90. lgbasallote

...clever

91. amistre64

i think if i get anymore fans the site will collapse into an infinitly large black hole tho so be careful if you do :)

92. amistre64

have you gone over how to find the terms used: a, d, n ?

93. helpmeplz311

yes

94. amistre64

good, cause one you know how to get those, the rest is just simple arithmetic

95. amistre64

*cause once you know

96. helpmeplz311

d common difference

97. amistre64

how do you find the common difference of the sequence?

98. helpmeplz311

subtract.

99. amistre64

right, subtract the first term from the second term problem 10: 7 ,13, 19, ... d = 13-7 = 6 right?

100. helpmeplz311

yes sirr

101. amistre64

and what does the "a" in the formula refer to?

102. helpmeplz311

a refers to a term

103. amistre64

yes, but there is "a" special a that we need to use in the formula itself. the FIRST term. In the problem im working thru, that would be: 7 d=6, a=7 and what does "n" mean?

104. amistre64

im going to use a different but equal notation for the formula: \[f(n)=a+d(n-1)\] \[f(n)=7+6(n-1)\]

105. amistre64

you can replace \(f(n)\) with \(a_n\) if you want, its just a placeholder

106. amistre64

the "n" is reserved for the position of the term we want to find. in this case, the 90th term \[f(n)=7+6(n-1)\] \[f(90)=7+6(90-1)\] \[f(90)=7+6(89)\] \[f(90)=7+534\] \[f(90)=541\]

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