Question

Does anyone know how to do this Sigma Notation question?

Answer 1

This

Answer 2

ok.
your common ratio (r) is?
your first term (\(a_1\)) is?
your number of terms (n) is?

Answer 3

I have absolutely no clue how to figure out those thing my teacher never taught me

Answer 4

@SolomonZelman

Answer 5

So you can't answer any of the questions I asked?

Answer 6

No :(

Answer 7

what is this: \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=1?

Answer 8

-2?

Answer 9

\(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\)
when n=1: \(\large\color{black}{ \displaystyle2(-2)^{1-1} =2(-2)^0=2\cdot 1=2}\)

Answer 10

Ok, can you tell me what is \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=2?

Answer 11

plug in 2 instead of n....

Answer 12

-4?

Answer 13

@SolomonZelman

Answer 14

yes

Answer 15

ok, now do the same when n=3

Answer 16

8

Answer 17

yes.

Answer 18

So so frar your terms are:
2, -4, 8....

do you notice any pattern?

Answer 19

you multiply times -2 every time, is this correct?

Answer 20

yes'

Answer 21

Ok, and this number by which you multiply every time (if a sequence is like yours, that follows a multiplication pattern), is called "common ratio" and is denoted by letter r.

Answer 22

So, we can say that r=-2

Answer 23

Now, what does your sequence start from, what is the first term?

Answer 24

2

Answer 25

yes

Answer 26

so we can say that the first term is 2. \(a_1=2\)

-----------------------------
(NOTATIONS)
A first term is denoted by \(a_1\)
Second term is denoted by \(a_2\)
Third term is denoted by \(a_3\)
any nth term is denoted by \(a_n\)
-----------------------------

Answer 27

And then your number of terms is 7 (i colored it in blue)
\(\Large\color{black}{ \displaystyle \sum_{ n=1 }^{\color{blue}{7}} 2(-2)^{n-1} }\)

Answer 28

so, now, again, pliz answer my 3 questions that I asked in the very beginning.

Answer 29

your common ratio (r) is? -2
your first term (a1) is? 2
your number of terms (n) is? 7

Answer 30

@SolomonZelman

Answer 31

do you still need help on this ?

Answer 32

you can use the formula \[a_1 \cdot \frac{1-r^{n}}{1-r}\]
and enter in all that info you and @solomonzelman found together

Answer 33

My power went off for a couple of hours due to a rail. I don't even think that "rail" is a good name for what happened... in any case; my apologies, and good luck!

Answer 34

and the answers to my initial 3 questions are correct, good job.