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 2 years ago
Can someone help with this? :)
It is posted below in the comment section so I can use the Equation editor.
 2 years ago
Can someone help with this? :) It is posted below in the comment section so I can use the Equation editor.

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sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1362285707700:dw\[\Sigma \]

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Find the sum of the arithmetic series! Pleassse help:)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1\(\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\) and a constant (here, 5) can be taken out of sum sign... :)

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Where r we getting this formula? I'm confused where to start

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1thats a standard formula that can be used.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1do you want a formula for sum of terms in arithmetic series ? its equivalent to this formula

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0Deriving the formula for an arithmetic series?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Yes that is the formula for the arithmetic series. Where do we go from there?:)

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0Well, maybe best to use this formula instead \[\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\] It's simpler :D

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0So anyway, this sum is just... dw:1362286375802:dw right?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ok, 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 : \(S_n = (n/2)(2a+(n1)d)\)

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0terenzreignz...how do you get these expanded form answer? Can u explain that? sorry

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0It is isn't the right answer in the back of the book

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0That's just kind of the definition. Or you could say the sigma notation is a compact form of the sum. \[\huge \sum_{k=1}^n=1+2+3+...+(n1)+n\] Basically adding all integers starting at 1 to n.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge \sum_{k=1}^nk=1+2+3+...+(n1)+n\] Bloody typo, sorry :)

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0So anyway, we can rearrange...dw:1362286994735:dw

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0And notice that these terms...dw:1362287037927:dw When added, they all equal n+1

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0what is the final answer? the answer is supposed to be 25,250...I just don't know how to get it

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1did you try any one of the 2 formula i gave u ??

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Going 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)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1oh, 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 ?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0So i fill in that question mark spot with 100? Im not sure

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1general term =5k with k=100, last term = 5*100 = 500 _

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0To clarify, this is the formula I am using. \[S _{n}=\frac{ n(t _{1}+ t _{n} )}{ 2 }\]

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0wait how does k =100 again?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1yup, 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)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1lower limit givs first term, upper limit gives last term

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0ok so 100 is the last term... And why do we multiply it by 5?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1last value of k is 100 general term = 5k so last term = 5*100

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0and the difference between the numbers would be five right? or is it something else

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1yes, common difference = 2nd term 1st term = 3rd term 2nd term =.... = 105 = 1510 =.... = 5 but thats not required for the formula you are using

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Oh ok that makes sense now. Maybe you should help me on other problems I post. Your a good help!

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ok, sure, but did u get 25250 for this one ?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Oh wait quick question! What was \[t _{1}\] in this equation

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1t1 is the 1st term index represents which term

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0the index is which part again?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1index is written as subscript \(\huge t_n\) here n is index and represent which term, t1 = 1st term, t2 =2nd term, and so on

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1yup. as 5 is the 1st term

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0ok 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

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait my bad! i got it

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1you mean in \(S_n = n (t_1+t_n)/2\) thats a general formula, do you want a derivation of this ?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0What would happen when I solve for \[t _{n}\] in an equation where n did not equal 1 and it equaled something else?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1didn'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

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1362289579021:dw Like this. N does not equal 1

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1i think u have made up this question ? or is it from your book/notes ?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0here Ill give you one from the book. dw:1362289721775:dw

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0thats 30 m by the way. It kinda got cut off

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1so, here your 1st term will start from m=10 in 30m and last term you'll get by putting m=20 in 30m

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0so how would i get \[t _{n}\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1tm = last term, last m =30 so to get last term tm, put m=30 in general term 30m is this confusing ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1general term tm =30m fist term t10 = 3010 (put m=10) last term t20 = 3020 (put m=20)

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0so I would do 30 10 first , and when do I do the 20? i dont know if that makes sense

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0ok lets not do this problem.. Ill ask my teacher on monday..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1you have formula, you have n, you have 1st term, u have last term....just plug in values! ohh..ok, as u wish

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0Ill be posting other problems so u may help me if u want
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