## sparky16 Group Title Can someone help with this? :) It is posted below in the comment section so I can use the Equation editor. one year ago one year ago

1. sparky16 Group Title

|dw:1362285707700:dw|$\Sigma$

2. sparky16 Group Title

Find the sum of the arithmetic series! Pleassse help:)

3. hartnn Group Title

$$\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}$$ and a constant (here, 5) can be taken out of sum sign... :)

4. sparky16 Group Title

Where r we getting this formula? I'm confused where to start

5. hartnn Group Title

thats a standard formula that can be used.

6. hartnn Group Title

do you want a formula for sum of terms in arithmetic series ? its equivalent to this formula

7. terenzreignz Group Title

Deriving the formula for an arithmetic series?

8. sparky16 Group Title

Yes that is the formula for the arithmetic series. Where do we go from there?:)

9. sparky16 Group Title

to find the sum?

10. terenzreignz Group Title

Well, maybe best to use this formula instead $\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}$ It's simpler :D

11. terenzreignz Group Title

So anyway, this sum is just... |dw:1362286375802:dw| right?

12. hartnn Group Title

ok, i'll mention the sum of arithmetic series formula also, then you choose which one you wanna use, the series will be 5,10,15,20,.... right ? (with n= 100 terms) he 1st term a1 = 5 and there's a common difference of d=5 then the sum formula is : $$S_n = (n/2)(2a+(n-1)d)$$

13. sparky16 Group Title

terenzreignz...how do you get these expanded form answer? Can u explain that? sorry

14. sparky16 Group Title

It is isn't the right answer in the back of the book

15. terenzreignz Group Title

That's just kind of the definition. Or you could say the sigma notation is a compact form of the sum. $\huge \sum_{k=1}^n=1+2+3+...+(n-1)+n$ Basically adding all integers starting at 1 to n.

16. terenzreignz Group Title

$\huge \sum_{k=1}^nk=1+2+3+...+(n-1)+n$ Bloody typo, sorry :)

17. terenzreignz Group Title

So anyway, we can rearrange...|dw:1362286994735:dw|

18. terenzreignz Group Title

And notice that these terms...|dw:1362287037927:dw| When added, they all equal n+1

19. sparky16 Group Title

what is the final answer? the answer is supposed to be 25,250...I just don't know how to get it

20. hartnn Group Title

did you try any one of the 2 formula i gave u ??

21. sparky16 Group Title

Going back to hartnn's response near the beginning. This is like the only formua I'm understanding how to do. $S _{100}= (100(5 + ?))/2$ I'm just confused how to get that number I didn't fill in? It's supposed to be $t _{n}$ (which is last term)

22. sparky16 Group Title

Anyone?

23. hartnn Group Title

oh, you need last term ? the general term is 5k to get last term, just put k=100 in general term so, what u get as last term ?

24. sparky16 Group Title

So i fill in that question mark spot with 100? Im not sure

25. hartnn Group Title

general term =5k with k=100, last term = 5*100 = 500 -_-

26. sparky16 Group Title

To clarify, this is the formula I am using. $S _{n}=\frac{ n(t _{1}+ t _{n} )}{ 2 }$

27. sparky16 Group Title

wait how does k =100 again?

28. hartnn Group Title

yup, thats the only other i didn't mention :P because you are summing from k=1 (which is 1st term) to k=100 (WHICH IS LAST TERM)

29. hartnn Group Title

lower limit givs first term, upper limit gives last term

30. sparky16 Group Title

ok so 100 is the last term... And why do we multiply it by 5?

31. hartnn Group Title

last value of k is 100 general term = 5k so last term = 5*100

32. sparky16 Group Title

and the difference between the numbers would be five right? or is it something else

33. hartnn Group Title

yes, common difference = 2nd term -1st term = 3rd term -2nd term =.... = 10-5 = 15-10 =.... = 5 but thats not required for the formula you are using

34. sparky16 Group Title

Oh ok that makes sense now. Maybe you should help me on other problems I post. Your a good help!

35. hartnn Group Title

ok, sure, but did u get 25250 for this one ?

36. sparky16 Group Title

Oh wait quick question! What was $t _{1}$ in this equation

37. hartnn Group Title

t1 is the 1st term index represents which term

38. hartnn Group Title

tn is the n'th term

39. sparky16 Group Title

the index is which part again?

40. hartnn Group Title

index is written as subscript $$\huge t_n$$ here n is index and represent which term, t1 = 1st term, t2 =2nd term, and so on

41. sparky16 Group Title

so t1 is 5

42. hartnn Group Title

yup. as 5 is the 1st term

43. hartnn Group Title

any more doubts ?

44. sparky16 Group Title

ok im sorry so I'm trying to solve it on paper. And I'm confused again.. how did we get $t _{n}$ in the formula

45. sparky16 Group Title

oh wait my bad! i got it

46. hartnn Group Title

you mean in $$S_n = n (t_1+t_n)/2$$ thats a general formula, do you want a derivation of this ?

47. hartnn Group Title

oh u got it ? good :)

48. sparky16 Group Title

What would happen when I solve for $t _{n}$ in an equation where n did not equal 1 and it equaled something else?

49. hartnn Group Title

didn't get your question ? do u have specific example for that ? say, if you want to find $$t_5$$, then u put n=5 in general term tn

50. sparky16 Group Title

|dw:1362289579021:dw| Like this. N does not equal 1

51. hartnn Group Title

i think u have made up this question ? or is it from your book/notes ?

52. sparky16 Group Title

53. sparky16 Group Title

here Ill give you one from the book. |dw:1362289721775:dw|

54. sparky16 Group Title

thats 30- m by the way. It kinda got cut off

55. hartnn Group Title

so, here your 1st term will start from m=10 in 30-m and last term you'll get by putting m=20 in 30-m

56. sparky16 Group Title

so how would i get $t _{n}$

57. hartnn Group Title

tm = last term, last m =30 so to get last term tm, put m=30 in general term 30-m is this confusing ?

58. sparky16 Group Title

kinda

59. hartnn Group Title

general term tm =30-m fist term t10 = 30-10 (put m=10) last term t20 = 30-20 (put m=20)

60. sparky16 Group Title

so I would do 30 -10 first , and when do I do the 20? i dont know if that makes sense

61. hartnn Group Title

it doesn't -_-

62. sparky16 Group Title

ok lets not do this problem.. Ill ask my teacher on monday..

63. hartnn Group Title

you have formula, you have n, you have 1st term, u have last term....just plug in values! ohh..ok, as u wish

64. sparky16 Group Title

Ill be posting other problems so u may help me if u want