anonymous
  • anonymous
Does anyone know how to do this Sigma Notation question?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
This
SolomonZelman
  • SolomonZelman
ok. your common ratio (r) is? your first term (\(a_1\)) is? your number of terms (n) is?
anonymous
  • anonymous
I have absolutely no clue how to figure out those thing my teacher never taught me

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anonymous
  • anonymous
@SolomonZelman
SolomonZelman
  • SolomonZelman
So you can't answer any of the questions I asked?
anonymous
  • anonymous
No :(
SolomonZelman
  • SolomonZelman
what is this: \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=1?
anonymous
  • anonymous
-2?
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=1: \(\large\color{black}{ \displaystyle2(-2)^{1-1} =2(-2)^0=2\cdot 1=2}\)
SolomonZelman
  • SolomonZelman
Ok, can you tell me what is \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=2?
SolomonZelman
  • SolomonZelman
plug in 2 instead of n....
anonymous
  • anonymous
-4?
anonymous
  • anonymous
@SolomonZelman
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
ok, now do the same when n=3
anonymous
  • anonymous
8
SolomonZelman
  • SolomonZelman
yes.
SolomonZelman
  • SolomonZelman
So so frar your terms are: 2, -4, 8.... do you notice any pattern?
SolomonZelman
  • SolomonZelman
you multiply times -2 every time, is this correct?
anonymous
  • anonymous
yes'
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
So, we can say that r=-2
SolomonZelman
  • SolomonZelman
Now, what does your sequence start from, what is the first term?
anonymous
  • anonymous
2
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
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 \(a_n\) -----------------------------
SolomonZelman
  • SolomonZelman
And then your number of terms is 7 (i colored it in blue) \(\Large\color{black}{ \displaystyle \sum_{ n=1 }^{\color{blue}{7}} 2(-2)^{n-1} }\)
SolomonZelman
  • SolomonZelman
so, now, again, pliz answer my 3 questions that I asked in the very beginning.
anonymous
  • anonymous
your common ratio (r) is? -2 your first term (a1) is? 2 your number of terms (n) is? 7
anonymous
  • anonymous
@SolomonZelman
freckles
  • freckles
do you still need help on this ?
freckles
  • freckles
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
SolomonZelman
  • SolomonZelman
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!
SolomonZelman
  • SolomonZelman
and the answers to my initial 3 questions are correct, good job.

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