OpenStudy (anonymous):

PLEASE HELP!! (Algebra 2) **I always give a medal to the person with the best answer** Find the sum of a finite arithmetic sequence from n = 1 to n = 10, using the expression 3n − 8. 56 85 54 116

3 years ago
OpenStudy (kirbykirby):

85

3 years ago
OpenStudy (kirbykirby):

This is because you are doing this: \[\sum_{n=1}^{10} (3n-8)=[3(1)-8] + [3(2)-8] +\ldots [3(10)-8]\]

3 years ago
OpenStudy (anonymous):

Thank you very much! This was so helpful (: Do you think you could help me with another one?

3 years ago
OpenStudy (kirbykirby):

sure

3 years ago
OpenStudy (anonymous):

Find the 12th partial sum of the summation of negative 7i plus 22, from i equals 1 to infinity.

3 years ago
OpenStudy (anonymous):

Hopefully that makes sense

3 years ago
OpenStudy (kirbykirby):

This is essentially asking for \[\sum_{i=1}^{12} (7i+22)=7\sum_{i=1}^{12}i+\sum_{i=1}^{12}22=7\left[\frac{12(13)}{2}\right]+12(22)\]

3 years ago
OpenStudy (anonymous):

for an arithmetic sequence we have\[S_n=\frac{ n }{ 2 }(a_1+a_n)\] you know n = 10, and \(a_n=3n-8\text{ making }a_1=-8\text{ and } a_{10} = 3(10)-8 = 22\) so you can find \(S_{10}\) by plugging in for

3 years ago
OpenStudy (anonymous):

\(n, a_1\text{ and } a_{10}\)

3 years ago
OpenStudy (anonymous):

I have no idea how to solve that @kirbykirby

3 years ago
OpenStudy (kirbykirby):

Oh the term in the brackets [ ], is for the sum of consecutive integers. The formula is \[\large \sum_{i=1}^ni =\frac{n(n+1)}{2}\]

3 years ago
OpenStudy (anonymous):

Oh and I just realized that when I copied the question, it put a 7 instead of a 4. Underneath the E it's supposed to say i = 4

3 years ago
OpenStudy (anonymous):

KNow what I mean?

3 years ago
OpenStudy (anonymous):

\[S_{10}=\frac{10}{2}(22+(-8))=5(14)=70\]

3 years ago
OpenStudy (anonymous):

@pgpilot326 If you are responding the the original question, that is not any of my answer choices.

3 years ago
OpenStudy (kirbykirby):

Oh like \[\sum_{i=4}^{12}\]

3 years ago
OpenStudy (kirbykirby):

I realized I forgot the negative in -7i

3 years ago
OpenStudy (anonymous):

Yes and the infinite sign is on top

3 years ago
OpenStudy (anonymous):

and then after that, it is -2i-10

3 years ago
OpenStudy (anonymous):

yeah sorry, \(a_1 = -5\text{ not } -8\) \[S_{10}=\frac{ 10 }{ 2 }(22+(-5))=5(17)=85\] again, sorry about that.

3 years ago
OpenStudy (anonymous):

It's okay (: Thank you though (: @pgpilot326

3 years ago
OpenStudy (anonymous):

@kirbykirby I would set it up properly, but I don't know exactly how to use the equation thingy lol

3 years ago
OpenStudy (kirbykirby):

So you never saw the formula \[\sum_{i=1}^n i=\frac{n(n+1)}{2}\] ?

3 years ago
OpenStudy (anonymous):

No, no I have! I meant I don't know how to set it up on open study

3 years ago
OpenStudy (kirbykirby):

ohh I see. Well one thing that might help is to press the "Equation" button below. If you press the Sigma/sum button for example, it will show some latex code like " sum_{?}^{?}" and you can replace the "?" with the upper and lower bounds of the sigma

3 years ago
OpenStudy (kirbykirby):

But ok if you are starting at i=4, and we want the 12th partial sum, that mean we would need to go from i=4 to 15 (as there are 12 terms between 4 and 15 if that makes sense)

3 years ago
OpenStudy (kirbykirby):

is -534 in your answers

3 years ago
OpenStudy (anonymous):

Yes, that does make sense and let check! (:

3 years ago
OpenStudy (anonymous):

No, it isn't. Here is what my answer choices are: 25 40 -348 72

3 years ago
OpenStudy (kirbykirby):

Hm. Ok um They gave you \[\sum_{i=4}^{\infty} (-7i+22)\], and they want the 12th partial sum of this?

3 years ago
OpenStudy (anonymous):

instead of -7i, it should be -2i and instead of +22 it should be -10. There aren't any parenthesis in their equation either

3 years ago
OpenStudy (kirbykirby):

\[\sum_{i=4}^{\infty} -2i-10\]

3 years ago
OpenStudy (anonymous):

I didn't realize how much I messed up when I sent the question. Not sure where the -7 and 22 came from when I copied the question. I apologize!

3 years ago
OpenStudy (anonymous):

and yes! That is it!

3 years ago
OpenStudy (kirbykirby):

I only get -348 if I include the parentheses

3 years ago
OpenStudy (kirbykirby):

\[\sum_{i=4}^{15} (-2i-10)=-348\]

3 years ago
OpenStudy (anonymous):

Maybe they forgot the parentheses? That is a answer choice though

3 years ago
OpenStudy (kirbykirby):

Perhaps. It's a bit sloppy to forget the parentheses because \[\sum_{i=4}^{\infty} -2i-10 \ne \sum_{i=4}^{\infty} (-2i-10)\], because without the parentheses, the -10 part is technically not included in the summation.

3 years ago
OpenStudy (kirbykirby):

But I'm pretty sure they mean the expression with the parentheses. Because without them, none of the answers match.

3 years ago
OpenStudy (anonymous):

That has to be it then. There has been more than 1 question with typos and answers that were all wrong, so this doesn't surprise me lol

3 years ago
OpenStudy (kirbykirby):

Hehe oh dear. But yeah. To actually calculate it though.. \[\sum_{i=4}^{15}( -2i-10)=-2 \sum_{i=4}^{15}i-\sum_{i=4}^{15}10\]

3 years ago
OpenStudy (anonymous):

Thank you so, so much! I have one more that should be easy, but I keep getting the wrong answer. Care to help once more? :p

3 years ago
OpenStudy (kirbykirby):

sure

3 years ago
OpenStudy (anonymous):

What is the sum of the arithmetic sequence 151, 137, 123, …, if there are 26 terms? −676 −650 −624 −598

3 years ago
OpenStudy (anonymous):

I keep getting -199 and that is not even close to any of those answers :l

3 years ago
OpenStudy (kirbykirby):

-199 is the 26th term, but it is not the sum of all the terms. So essentially you found: 151, 137, 123, ..., -185, -199

3 years ago
OpenStudy (kirbykirby):

you now need to add up all of these terms together

3 years ago
OpenStudy (anonymous):

OH! okay! Let me do that really quick (:

3 years ago
OpenStudy (anonymous):

I got -599

3 years ago
OpenStudy (kirbykirby):

I get -624

3 years ago
OpenStudy (anonymous):

I'm doing it again. I'm most likely wrong lol

3 years ago
OpenStudy (kirbykirby):

ok

3 years ago
OpenStudy (anonymous):

I ended up with -624 too

3 years ago
OpenStudy (kirbykirby):

awesome =)

3 years ago
OpenStudy (anonymous):

I must have skipped a few before

3 years ago
OpenStudy (anonymous):

Thank again for your help!!

3 years ago
OpenStudy (kirbykirby):

no problem :)

3 years ago