Question

When finding the sum of the arithmetic series 4 + 1 + -2 + -5 + -8 + -11, you will have a step of work that contains the number -3. Use complete sentences to describe how the -3 was calculated and what it means.

Answer 1

4+1 = 5
4+1-2 = 3
4+1-2-5=-2
4+1-2-5-8=-10
4+1-2-5-8-11=-21

So clearly there isn't a -3 in this whole process. Something seems off, but idk what.

Answer 2

wait so do you just add all of the numbers to find the sum?

Answer 3

yes because "sum" means "result after addition"

Answer 4

I'm not sure where they're getting -3 though...

Answer 5

ha i'm so confused?

Answer 6

yeah same here, so there has to be a typo

Answer 7

that's my guess

Answer 8

okay, thank you!!

Answer 9

np, sorry I couldn't be of more help

Answer 10

that's okay, i appreciate it :)

Answer 11

SmallChain, that's something for a private message and it's not really relevant.

Answer 12

^truth, do you understand this smallchain??

Answer 13

Know how to find the equation for an arithmetic series?

Answer 14

http://www.regentsprep.org/regents/math/algtrig/ATP2/ArithSeq.htm

Answer 15

i still don't really understand. do you think you could walk me through it please?

Answer 16

Well I think , it is the common difference which is equal to (-3)

Answer 17

Do you see the sequence of numbers? 4, 1, -2, -5, -8, -11

Yes. That is the part I was going to point out.

Answer 18

And the step that involves the use of "-3" is :

\(S_n = \cfrac{n}{2} ( 2a + (n-1)d ) \)

where S_n = sum of n-terms

n = no. of terms
a = first term
d = common difference.

Answer 19

It is actually , Arithmetic Progression (as said earlier by @e.mccormick ) .

@girlscum - Are you getting my point?

Answer 20

You look at each step, and what number added to a step in the sequence would get you to the next step? That is the common difference. So you can find it using any two steps and check it with any two others.

4+d=1, solve for d.
then -5 + (-3) = -8 to check.

Answer 21

So write about that and you will have your answer.

Answer 22

i think i understand.. how exactly are you finding the common difference though? sorry i'm terrible at these problems.

Answer 23

You can find the common difference by subtracting the two consecutive terms :

a_1 , a_2 , ... , a_n

common diff. = a_2 - a_1 = a_3 - a_2 = .... = a_n - a_(n-1)

Answer 24

so the answer would be -3 is the common difference?

Answer 25

Not actually,you will have to explain how u calculated -3 and what is common difference.

Answer 26

okay so you'd subtract consecutive terms to find the common difference which is -3?

Answer 27

Yeah, it is -3 here.

Answer 28

For example :

Let us take a series : 2,4,6,8

common difference = 4-2 = 6-4 = 8 - 6 = 2

Answer 29

okay i get it now thank you both so much! do you think you could help me with some other problems?

Answer 30

Well, I think, I can! I will try my best :)

Also, Since you are new to OpenStudy : Welcome to OpenStudy.

Answer 31

thank you! hold on one sec let me find just get my work out

Answer 32

What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?

Answer 33

Use the formula : \(S_n = \cfrac{n}{2} ( 2a + (n-1)d ) \)

Answer 34

how would i find d?

Answer 35

@mathslover

Answer 36

S_n = 9,374 (given)

n = 43

a = -13

put in the values and solve for d.

Answer 37

oh, my bad i misread the problem.

Answer 38

okay i think i did it completely wrong do you think you could walk me through it haha

Answer 39

if it helps the answer has to be one of these
11
11.5
12
12.5

Answer 40

@mathslover