Question

Write the sum using summation notation, assuming the suggested pattern continues.

-9 - 3 + 3 + 9 + ... + 81

summation of the quantity negative nine plus six n from n equals zero to fifteen
summation of negative fifty four times n from n equals zero to fifteen
summation of negative fifty four times n from n equals zero to infinity
summation of the quantity negative nine plus six n from n equals zero to infinity

Answer 1

Can you tell me what the difference is?

Answer 2

+6

Answer 3

yes.

Answer 4

What is the \(\large\color{blue}{ a_1}\) ?

Answer 5

-9

Answer 6

Yes,
So you would need to find "what number of term is 81 in a sequence"

There is a formula, (which you have already seen most likely).
\(\large\color{blue}{ a_n=a_1+d(n-1)}\)

Fill in the numbers,
\(\large\color{blue}{ 81=(-9)+6(n-1)}\)

Answer 7

Solution for \(\large\color{blue}{ n}\) will give you the the answer, for which(th) term in a sequence is 81.

Answer 8

16?

Answer 9

yes, I will go over just in case.
\(\large\color{blue}{ 81=(-9)+6(n-1)}\)
\(\large\color{blue}{ 90=6(n-1)}\)
\(\large\color{blue}{ 15=n-1}\)
\(\large\color{blue}{ 16=n}\)

Answer 10

So you know that \(\large\color{blue}{ 81}\) is the \(\large\color{blue}{ a_{16}}\)

Answer 11

You have:

\(\large\color{blue}{ a_{1}=-9}\)

\(\large\color{blue}{ d=6}\)

\(\large\color{blue}{ 81}\) is the \(\large\color{blue}{ a_{16}}\)

Answer 12

You want to write the sum for this pattern assuming (where the dots in the questions are, i.e. +3, + 9 ... + 81 )
THAT the pattern is going on (that you add +6 each time).

Answer 13

You are starting from an index (on the bottom of the \(\large\color{blue}{ \Sigma}\) ) of n=0.

Answer 14

(as your options say.

Answer 15

\(\Large\color{royalblue}{ \displaystyle \sum_{ n=0 }^{ ? } ~~?}\)

Answer 16

i think the # on top is 15

Answer 17

Yes, correct.

Answer 18

Because if the first term is given when n=0 (since that is where the index starts)
then 16th would be given by n=15.

Answer 19

is the number on the side (-9+6n)

Answer 20

because -9 is where it starts

Answer 21

\(\Large\color{royalblue}{ \displaystyle \sum_{ n=0 }^{ 15 } (6n-9)}\)

Answer 22

yes, that seems correct.

Answer 23

I think its 6n+9, not -9

Answer 24

Why?

Answer 25

oh my bad

Answer 26

you had it arranged the other way

Answer 27

\(\Large\color{royalblue}{ \displaystyle \sum_{ n=0 }^{ 15 } (-9+6n)}\) is how you wrote it, thinking about just how the terms go,

as, starting from -9. (And this is correct.)

I re-wrote it as, \(\Large\color{royalblue}{ \displaystyle \sum_{ n=0 }^{ 15 } (6n-9)}\)

Answer 28

you're correct

Answer 29

yes, just that \(\Large\color{royalblue}{ \displaystyle \sum_{ n=0 }^{ 15 } (6n-9)}\) uses less "buttons" than \(\Large\color{royalblue}{ \displaystyle \sum_{ n=0 }^{ 15 } (-9+6n)}\)

Answer 30

it is all same though:)

Answer 31

just as saying:
y=xm-b
and
y=-b+xm

Answer 32

but very well done, so all we did was, that we found the differences and the first term.
Then found which(th) number is the last term in the sequence.

After this we wrote the summation.

Answer 33

I know, i wasn't paying attention

Answer 34

Yw:)

Answer 35

YOu actually came up with a pattern really well!

Answer 36

you did a good job helping!

Answer 37

That is why I am here.... doing my best:)