Question

Please help! I don't get arithmetic sequences!

What is the sum of the finite arithmetic series?
(-10)+0+10+20+...+130

Answer 1

Do you know what a common difference is ? and how to find it ?

Answer 2

No, I don't. THAT'S what I'm trying to figure out. Do I just keep adding them together or subtract?

Answer 3

In arithmetic sequence, when you add a certain number to a term, you get the next term.

example :
2,5,8,11,....
here if i add 3 to each term, i would get the next term!

does this make sense ?

Answer 4

Yes, so far.

Answer 5

(-10)+0+10+20+...+130

what would i add to each termof this sequence to get the next term ?

Answer 6

-10 right? Because -10+0=-10.

Answer 7

sure ?

one of the term is 10,
you would add +10 or -10 to get the next term 20 ?

Answer 8

+10. So I just keep adding +10 until I get the next term (+130)?

Answer 9

this was only for you to find the "common difference" d of the arithmetic sequence!

so if you add +10 to each term, you get the next term,
thats why your common difference d = 10
got this so far ?

Answer 10

Yes. So far, so good.

Answer 11

cool :)

now the sum,
There is a ready-made sum formula for arithmetic sequence which you can use
\(\Large S_n = (n/2) [2a_1 +(n-1)d]\)
or
\(\Large S_n = (n/2)[a_1 +a_n]\)

where,
n = number of terms
a1 = 1st term = - 10 here
an = last term
f = common difference = d =10 here

Answer 12

either case , now we just need to find 'n'
which is how many terms are there in the sequence, any ideas ?

Answer 13

Sorry I'm taking so long. I'm trying to figure it out on paper too.

(a+10) (a+2(10)) is how i wrote it out to solve it right?

Answer 14

So how exactly do i find 'n'? I'm totally lost!!!

Answer 15

there are 2 ways,

you can find 'n' mentally...
10 is 3rd term
20 is 4th term
30 is 5th term

and so on...

continuing this pattern,
100 will be 12th term!
110 will be 13th term
120 will be 14th term
and lastly
130 will be 15th term

makes sense ?

Answer 16

the other way is to use the n'th term formula,
\(a_n = a_1 +(n-1)d\)

but if you got that above way to find 'n', lets not go into this

Answer 17

Ooooooooh! I've got it so far!

Answer 18

and is that other way more difficult?

Answer 19

excellent!

so now we have all the terms of that sum formula.
and no, the other method is also easy! i will tell you other method to get 'n' after we finish finding sum

Answer 20

use any one of the sum formulas
n = 15
a1 = 1st term = -10
an = last term = 130
d = common difference = 10

Answer 21

the 2nd formula is easier, you can try that first

Answer 22

Okay, this is what I have so far:

sn=n(a1+an)/2

s15=15(-10+130)/2

Answer 23

going good :)

Answer 24

Okay I got:
s15=900. Did I do that right?

Answer 25

very good!
900 is the correct sum! :D

Answer 26

now for that other way of finding 'n'

we know last term = 130, an = 130
d = 10
a1 = 1st term = -10

formula : \( \large a_n = a_1 + (n-1)d \\ \large 130=-10+(n-1)10 \\ 130+10 = 10 (n-1) \\ 140 = 10 (n-1)\\ 14 = n-1 \\ n = 14+1 =15 \)

thats how you get number of terms = 15

Answer 27

Ooooooooh! I think I like this way better! I'll have to practice it more for future reference! :) Thank you very much!

Answer 28

most welcome ^_^
you can go through this link for better understanding of sequences :)

http://openstudy.com/study#/updates/503bb2a0e4b007f9003103b0

Answer 29

Thanks again! Have an awesome night!

Answer 30

you too :)
and have the sweetest dreams :)