Question

can someone walk me through this?
what is the sum of the finite arithmetic series? (-15)+0+15+30...+195

Answer 1

okay, what is the difference in the sequence ?

Answer 2

+15

Answer 3

yes.

Answer 4

So, you add 15 every time

Answer 5

And you start from -15

Answer 6

Can you think of a line with a slope of 15 (common difference 15) and a y-intercept (-15)(the first term) ?

Answer 7

what will the equation of this line be ?

Answer 8

uh what?

Answer 9

y-intercept (or the first term) = -15
difference (or the slope) = 15

what is the equation of the line ?

Answer 10

(I am just trying to get you to think of a pattern that models the terms, and then we will do the sigma notation)

Answer 11

y=15x-15?

Answer 12

yes, exactly

Answer 13

now, we need to see whichTH term is 195

Answer 14

\(\large\color{blue}{ \displaystyle a_n=a_1+d(n-1)}\)

\(\large\color{blue}{ \displaystyle 195=(-15)+15(n-1)}\)

see how I am setting it up?
Can you solve for "n" ?

(this n-solution is going to be the number of term that 195 has in the sequence)

Answer 15

196=n?

Answer 16

how so ?

Answer 17

oh wait

Answer 18

i see what i did

Answer 19

11=n?

Answer 20

the 15 (i plugged for a1) is negative
and you are adding n to both sides at the end

Answer 21

I mean adding 1 to both sides at the end

Answer 22

creative way
\(\large\color{blue}{ \displaystyle 195=(-15)+15(n-1)}\)

\(\large\color{blue}{ \displaystyle 195=15(n-1-1)}\)

\(\large\color{blue}{ \displaystyle 195=15(n-2)}\)

\(\large\color{blue}{ \displaystyle 13=n-2}\)

Answer 23

or, same way you can add 15 to both sides, and the divide both sides by 15, you would be getting
\(\large\color{blue}{ \displaystyle 14=n-1}\)

Answer 24

well let me show you how i did it so i can see what i did wrong

Answer 25

sure

Answer 26

\[195=(-15)+15(n-1)\]
\[195=(-15)+15n-15\]
\[195=-30+15n\] (i realized what i did wrong)..

Answer 27

i subtracted 30 instead of added it

Answer 28

225/15=15n/15

Answer 29

15=n

Answer 30

yes.
and sorry an accident happened

Answer 31

My young 12 year old brother plugged in a bare wire, into the plugin, and somewhere in a room I am sitting, and my comp shut down completely.

Fortunately, no one suffered of electric current...:)

Anyways

Answer 32

so you have 15 terms

from n=1 to n=15 OR from n=0 to n=14

Answer 33

\(\large\color{blueviolet}{ \displaystyle \sum_{ n=0 }^{ 14 } ~(15n-15)}\)

Answer 34

ohkay how do i begin with that

Answer 35

well, what I wrote is one possible answer (and I believe the most simple one

Answer 36

ell the answers its giving me are
1355
1350
1335
1000

Answer 37

i believe its 1350 but im not completely sure

Answer 38

I http://www.wolframalpha.com/input/?i=sum+from+n%3D0+to+n%3D14+%2815n-15%29

correct!