Question

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

Answer 1

85

Answer 2

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

Answer 3

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

Answer 4

sure

Answer 5

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

Answer 6

Hopefully that makes sense

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

I have no idea how to solve that @kirbykirby

Answer 11

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

Answer 12

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

Answer 13

KNow what I mean?

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

I realized I forgot the negative in -7i

Answer 18

Yes and the infinite sign is on top

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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)

Answer 27

is -534 in your answers

Answer 28

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

Answer 29

No, it isn't. Here is what my answer choices are:

25

40

-348

72

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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!

Answer 34

and yes! That is it!

Answer 35

I only get -348 if I include the parentheses

Answer 36

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

Answer 37

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

Answer 38

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.

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

sure

Answer 44

What is the sum of the arithmetic sequence 151, 137, 123, …, if there are 26 terms?

−676

−650

−624

−598

Answer 45

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

Answer 46

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

Answer 47

you now need to add up all of these terms together

Answer 48

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

Answer 49

I got -599

Answer 50

I get -624

Answer 51

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

Answer 52

ok

Answer 53

I ended up with -624 too

Answer 54

awesome =)

Answer 55

I must have skipped a few before

Answer 56

Thank again for your help!!

Answer 57

no problem :)