Question

Using sigma notation, describe the total length of 7 pictures hung side-by-side. Then find the total length the pictures occupy along the wall if the first picture has a length of 10 inches and the length of each successive picture is 4 inches longer than the previous one. (2 points) Using complete sentences, describe the characteristics and parts of sigma notation. Please also provide a unique example. (2 points) Using complete sentences, explain how sigma notation is connected to arithmetic sequences and series. (2 points)

Answer 1

start basic
first on is 10 then 12,14,16,18, 20, 22
total length is therefore
\[10+12+14+16+18+20+22\]

Answer 2

"Sigma notation", but I know you are typing that. I like interfering between geniuses, y'know?

Answer 3

lots of ways to write in sigma notation
you could say
\[\sum_{n=0}^610+2n\] for example

Answer 4

I only really need the first question.

Answer 5

is it asking me for 2 answers?

Answer 6

he is giving u da ancer be pashent

Answer 7

I was just asking o_o, sorry.

Answer 8

or if you want to start at \(n=1\) you could write
\[\sum_{n=1}^710+2(n-1)\] or even
\[\sum_{n=1}^78+2n\]

Answer 9

Wait, you don't know how to start? You're saying if you want to start o.o...

Answer 10

at 1.

Answer 11

I'd stick to the last one. You derive the formula to start with, by the way.

Answer 12

what i meant was "what do you want the lower index of summation to be?"

Answer 13

Doesn't the question tell you?

Answer 14

ok all that stuff was wrong anyway because it says "4 inches" not 2 inches

Answer 15

Well, but the question doesn't ask what *Satellite* would like the lower index to be.

Answer 16

so write
\[\sum_{n=1}^7 6+4n\]

Answer 17

isn't it 4n-10?

Answer 18

that will give you
\[10+14+16+20+24+28+32\]

Answer 19

I meant 4n-4

Answer 20

because (n-1)(4)

Answer 21

?

Answer 22

It'd be whatever you like it to be, Daren, as long as it is correct.

Answer 23

oh wait your right

Answer 24

I forgot the a1

Answer 25

Ok thankyou, satellite73 :)

Answer 26

ParthKohli, you were no help -_-

Answer 27

\[a_1=10,a_2=10+4,a_3=10+8,...\]

Answer 28

I understand how to do it now :)

Answer 29

Of course I am not a help. I am just a sidekick haha!

Answer 30

Not a good sidekick <.<!

Answer 31

Anyone watch internet icon?

Answer 32

Rest must go to chat, and I be a sidekick only when Satellite is there. He's the boss. lol

Answer 33

I see why ...

Answer 34

I don't get what you do o.O

Answer 35

different authors start at different places; n=0 or n=1 is not set in stone

Answer 36

I just get confused what to say when Satellite is there. I'm a great help if he's not there. Haha!

Answer 37

I went back to the example and there's an understood 1 <.<

Answer 38

In previous examples just like it.

Answer 39

and n can't equal 0 <.< Idk where you got that from.

Answer 40

it tends to be easier to write it up with n=0, and just change all the ns to n-1 afterwards

Answer 41

I like sigma notation when \(n\) starts at 1.

Answer 42

No, bye.

Answer 43

thanks for help openstudy!

Answer 44

You're welcome!

Answer 45

n can, and often times does = 0 :/

Answer 46

Not from what I'm learning :/ I guess it's more advanced than algebra 2 or is in another lesson :/

Answer 47

there is a long lasting debate as to whether or not "0" is a natural number (n) or not, the debate has never been settled so different authors write their texts according to their own preferences.

http://www.wolframalpha.com/input/?i=natural+number

Answer 48

spose you calculating interest on an account that pays after the first year

a0 = original balance
a1 = balance in year 1
a2 = balance in year 2

as such n=0 is a perfered starting point.

Answer 49

calculating up sequences is also easier to start with n=0; but there is no big deal either way.

if you start with n=0 and want n=1; +1 to the index and -1 from the expression and the results are the adjusted for which ever one you wish to consider

Answer 50

\[\sum_{i=1}^{n}i = \frac{n(n+1)}{2};~1,3,6,10,15,...\]
\[\sum_{i=0}^{n}i = \frac{(n+1)(n+2)}{2};~1,3,6,10,15,...\]

Answer 51

STOP AMISTRE THIS IS COMPLETELY WRONG I ALREADY HAVE THE ANSWER T_T!

Answer 52

how strange :/

Answer 53

are you "yelling" becasue i have defended my position? or is this just some odd form of asking me to not reply?

Answer 54

Oh, I just like caps lol xD

Answer 55

the answer turns out being -60

Answer 56

ok, good luck with it ;)

Answer 57

oh wait 154

Answer 58

lol i was looking at #4

Answer 59

thanks for all the effort though :)