anonymous
  • anonymous
Can someone help with this? :) It is posted below in the comment section so I can use the Equation editor.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1362285707700:dw|\[\Sigma \]
anonymous
  • anonymous
Find the sum of the arithmetic series! Pleassse help:)
hartnn
  • hartnn
\(\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\) and a constant (here, 5) can be taken out of sum sign... :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Where r we getting this formula? I'm confused where to start
hartnn
  • hartnn
thats a standard formula that can be used.
hartnn
  • hartnn
do you want a formula for sum of terms in arithmetic series ? its equivalent to this formula
terenzreignz
  • terenzreignz
Deriving the formula for an arithmetic series?
anonymous
  • anonymous
Yes that is the formula for the arithmetic series. Where do we go from there?:)
anonymous
  • anonymous
to find the sum?
terenzreignz
  • terenzreignz
Well, maybe best to use this formula instead \[\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\] It's simpler :D
terenzreignz
  • terenzreignz
So anyway, this sum is just... |dw:1362286375802:dw| right?
hartnn
  • hartnn
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 : \(S_n = (n/2)(2a+(n-1)d)\)
anonymous
  • anonymous
terenzreignz...how do you get these expanded form answer? Can u explain that? sorry
anonymous
  • anonymous
It is isn't the right answer in the back of the book
terenzreignz
  • terenzreignz
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.
terenzreignz
  • terenzreignz
\[\huge \sum_{k=1}^nk=1+2+3+...+(n-1)+n\] Bloody typo, sorry :)
terenzreignz
  • terenzreignz
So anyway, we can rearrange...|dw:1362286994735:dw|
terenzreignz
  • terenzreignz
And notice that these terms...|dw:1362287037927:dw| When added, they all equal n+1
anonymous
  • anonymous
what is the final answer? the answer is supposed to be 25,250...I just don't know how to get it
hartnn
  • hartnn
did you try any one of the 2 formula i gave u ??
anonymous
  • anonymous
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)
anonymous
  • anonymous
Anyone?
hartnn
  • hartnn
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 ?
anonymous
  • anonymous
So i fill in that question mark spot with 100? Im not sure
hartnn
  • hartnn
general term =5k with k=100, last term = 5*100 = 500 -_-
anonymous
  • anonymous
To clarify, this is the formula I am using. \[S _{n}=\frac{ n(t _{1}+ t _{n} )}{ 2 }\]
anonymous
  • anonymous
wait how does k =100 again?
hartnn
  • hartnn
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)
hartnn
  • hartnn
lower limit givs first term, upper limit gives last term
anonymous
  • anonymous
ok so 100 is the last term... And why do we multiply it by 5?
hartnn
  • hartnn
last value of k is 100 general term = 5k so last term = 5*100
anonymous
  • anonymous
and the difference between the numbers would be five right? or is it something else
hartnn
  • hartnn
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
anonymous
  • anonymous
Oh ok that makes sense now. Maybe you should help me on other problems I post. Your a good help!
hartnn
  • hartnn
ok, sure, but did u get 25250 for this one ?
anonymous
  • anonymous
Oh wait quick question! What was \[t _{1}\] in this equation
hartnn
  • hartnn
t1 is the 1st term index represents which term
hartnn
  • hartnn
tn is the n'th term
anonymous
  • anonymous
the index is which part again?
hartnn
  • hartnn
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
anonymous
  • anonymous
so t1 is 5
hartnn
  • hartnn
yup. as 5 is the 1st term
hartnn
  • hartnn
any more doubts ?
anonymous
  • anonymous
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
anonymous
  • anonymous
oh wait my bad! i got it
hartnn
  • hartnn
you mean in \(S_n = n (t_1+t_n)/2\) thats a general formula, do you want a derivation of this ?
hartnn
  • hartnn
oh u got it ? good :)
anonymous
  • anonymous
What would happen when I solve for \[t _{n}\] in an equation where n did not equal 1 and it equaled something else?
hartnn
  • hartnn
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
anonymous
  • anonymous
|dw:1362289579021:dw| Like this. N does not equal 1
hartnn
  • hartnn
i think u have made up this question ? or is it from your book/notes ?
anonymous
  • anonymous
I made it up
anonymous
  • anonymous
here Ill give you one from the book. |dw:1362289721775:dw|
anonymous
  • anonymous
thats 30- m by the way. It kinda got cut off
hartnn
  • hartnn
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
anonymous
  • anonymous
so how would i get \[t _{n}\]
hartnn
  • hartnn
tm = last term, last m =30 so to get last term tm, put m=30 in general term 30-m is this confusing ?
anonymous
  • anonymous
kinda
hartnn
  • hartnn
general term tm =30-m fist term t10 = 30-10 (put m=10) last term t20 = 30-20 (put m=20)
anonymous
  • anonymous
so I would do 30 -10 first , and when do I do the 20? i dont know if that makes sense
hartnn
  • hartnn
it doesn't -_-
anonymous
  • anonymous
ok lets not do this problem.. Ill ask my teacher on monday..
hartnn
  • hartnn
you have formula, you have n, you have 1st term, u have last term....just plug in values! ohh..ok, as u wish
anonymous
  • anonymous
Ill be posting other problems so u may help me if u want

Looking for something else?

Not the answer you are looking for? Search for more explanations.