Question

find the sum of the given arithmetic series. (: PLEASE HELP ME!!!
1.30+23+16+9+...(-30)
2. 26+19+12+5+...+(-37)
3.27+20+13+6+...+(-36)

Answer 1

just use a caclulator lol

Answer 2

and it will give me the answers? lol

Answer 3

dont listen to @mitu12

Mathway is a site that gives the answers and doesnt explain. it does but you have to pay and sometimes you dont understand the concept.

Answer 4

ohhh okay thank you!

Answer 5

its like a calculator

Answer 6

The sum of an arithmetic series is given by:\[\Large\rm S_n=\frac{n(a_1+a_n)}{2}\]

Answer 7

We're given the last term and the first term.
The work we'll have to do is figuring out `how many` terms we have.
That is our \(\Large\rm n\) value.

Answer 8

The first is \(\Large\rm a_1=30\)
The common difference is \(\Large\rm d=a_2-a_1=-7\)

The general form for finding the nth term of a geometric sequence is given by:\[\Large\rm a_n=a_1+d(n-1)\]Plugging in our stuff gives us:\[\Large\rm a_n=30-7(n-1)\]

Answer 9

We know that our LAST term is -30.
Let's plug that in for our \(\Large\rm a_n\) and see which \(\Large\rm n\) value that corresponds to.
That will tell us how many terms we have.

Answer 10

\[\Large\rm -30=30-7(n-1)\]

Answer 11

Do you understand how to solve for n in that set up?

Answer 12

do i just try and get n by itself?

Answer 13

Yes, then we will have an \(\Large\rm n\) value for our \(\Large\rm S\) formula :)

Answer 14

okay!

Answer 15

Hmm it's not working out to an integer value.. this is really weird :o

Answer 16

Oh I see the problem.
The first one listed is NOT an arithmetic series.
One of the numbers is messed up.

We cant have 30 AND -30 in the series.
Did you copy it down correctly?
I assume you just copy/pasted, yes? :o

Answer 17

sorry i meant (-33)

Answer 18

Oh ok that would make more sense :3
So we're actually plugging it in like this:\[\Large\rm -33=30-7(n-1)\]

Answer 19

okay sorry about that again!!

Answer 20

-55n?

Answer 21

Hmmm, I'm not sure what you did there.

We're trying to isolate our n.\[\Large\rm -33=30-7(n-1)\]So start by subtracting 30 from each side,\[\Large\rm -63=-7(n-1)\]Divide by -7,\[\Large\rm 9=n-1\]Add 1 to each side,\[\Large\rm 10=n\]Understand those steps ok? :o

Answer 22

yes. lol

Answer 23

So now we have all of the information we need:
\(\Large\rm a_1=30, \qquad a_n=-33,\qquad n=10\)

Plug them into your formula for sum,\[\Large\rm S=\frac{n(a_1+a_n)}{2}\]What do you get for your sum? :)

Answer 24

-15

Answer 25

do you mind helping me with the other two? it is okay if you do not want too.

Answer 26

So you'll need to do these steps for all of them, so get comfortable with the process.
\[\Large\rm S=\frac{n(a_1+a_n)}{2}\]We need three things,
\(\Large\rm a_1,~ a_n,~n\)

We already have \(\Large\rm a_1,~a_n\)
In order to find \(\Large\rm n\), we have to first find the common difference and plug everything into our formula for the nth term.\[\Large\rm a_n=a_1+d(n-1)\]

Answer 27

So start by finding your common difference. (The second term minus the first term).
Then plug all that jazz into the formula to find your n.

Answer 28

okay thank you!!

Answer 29

You can do it mads! c:
Lemme know if you get stuck.
Look back at the steps we took also.

Answer 30

was the -15 correct? lol

Answer 31

For the first one?
Yes, good job c:

Answer 32

Thank you for all your help(:

Answer 33

i got -11 for the 2nd one and -9 for the 3rd. Do you mind checking to see if i got the correct answer? :)

Answer 34

For the second problem,
\[\Large\rm a_1+a_n=-11\]Did you forgot to multiply that by \(\Large\rm \dfrac{n}{2}\)?

Remember,\[\Large\rm S=\frac{n}{2}(a_1+a_n)\]

Answer 35

You have to find your n value :O

Answer 36

ive confused myself now i am lost..im so sorry.

Answer 37

i got,-10.57 but i think i did something wrong on my work.

Answer 38

What is the common difference?
\(\Large\rm d=?\)

Answer 39

-7

Answer 40

\[\Large\rm a_n=a_1+d(n-1)\]\[\Large\rm -37=26-7(n-1)\]And what'd you get for n? :d

Answer 41

-10.57?

Answer 42

Hmm, no.
Make sure you do the subtraction step before you do the division step.

Answer 43

okay, i see what i did wrong...

Answer 44

That's only half of the work though!
Remember you have to take your n value and plug it into the S formula.

Answer 45

nevermind i messed up again. i am so sorry.

Answer 46

lol :) dat mads

Answer 47

Is this step ok?