anonymous
  • anonymous
Given the geometric sequence where a1 = -3 and the common ratio is 9, what is the domain for n?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
OPTIONS All integers All integers where n ≥ -1 All integers where n ≥ 1 All integers where n ≥ 0
anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
@pooja195

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anonymous
  • anonymous
@perl
pooja195
  • pooja195
@SolomonZelman ;-; ?
SolomonZelman
  • SolomonZelman
Well, if you are starting from n=1, then your terms \(a_n\) can be: \(a_1\), \(a_2\), \(a_3\), \(a_4\),\(a_5\), and so forth.... To answers this question, you don't really need to know about the common ratio, or even what type of sequence it is. Nor do you have to know what the \(a_1\) is, as long as you know that is starts from \(a_1\) (i.e. from n=1).
SolomonZelman
  • SolomonZelman
All these: \(\large a_\color{red}{1}\), \(\large a_\color{red}{2}\), \(\large a_\color{red}{3}\), \(\large a_\color{red}{4}\), \(\large a_\color{red}{5}\), are values of n that are ?
anonymous
  • anonymous
Is it all integers?
SolomonZelman
  • SolomonZelman
Can you have \(\large a_{-1}\) ??
anonymous
  • anonymous
they are positive
SolomonZelman
  • SolomonZelman
yes, all positive integers, correct...
anonymous
  • anonymous
So its C?
SolomonZelman
  • SolomonZelman
So your answer choice is c, n≥1.
anonymous
  • anonymous
Thanks!
SolomonZelman
  • SolomonZelman
Also I can teach you how to put up ≥ ≤ ∞ and other symbols without copy pasting, want to know how?
SolomonZelman
  • SolomonZelman
it works on almost every site...
anonymous
  • anonymous
Can you help me with this questions: Given the arithmetic sequence an = -3 + 9(n - 1), what is the domain for n? OPTIONS: All integers where n ≥ 1 All integers All integers where n ≥ 0 All integers where n > 1
anonymous
  • anonymous
Is an arithmetic sequence always positive integers?
SolomonZelman
  • SolomonZelman
\(\large\color{blue}{ \displaystyle {\rm CODES,~~short~guide} }\) 1) Click and hold ALT 2) click the number code (using the numbers that are on the right of the keyboard, and `NOT` the ones below `F1`, `F2`, `F3`, etc., ) 3) release the ALT number code result `0 2 1 5 ` × `2 4 6 ` ÷ ` 7 ` • ──────────────── among with other symbols. code result 2 5 1 √ ` 7 5 4 ≥` 7 5 5 ≤ ` 2 4 1 or 7 5 3 ± ` 2 4 7 ≈ ` 0 1 8 5 ¹ ` 2 5 3 ² ` 0 1 7 9 ³ ` 1 6 6 ª ` 2 5 2 ⁿ ` 1 6 7 º ` 2 4 8 ° ` 0 1 5 3 ™ ` 0 1 9 0 ¾ ` 4 2 8 ¼ ` 1 7 1 ½ ` 2 2 7 π ` 1 5 5 ¢ ` 2 3 6 ∞ ` 1 5 9 ƒ `
SolomonZelman
  • SolomonZelman
Now as far as your question....
SolomonZelman
  • SolomonZelman
quoting your question: ``` Can you help me with this questions: Given the arithmetic sequence an = -3 + 9(n - 1), what is the domain for n? OPTIONS: All integers where n ≥ 1 All integers All integers where n ≥ 0 All integers where n > 1 ``` (end quote) Now, you are given that \(\large\color{black}{ \displaystyle a_n=-3+9(n-1) }\)
SolomonZelman
  • SolomonZelman
it doesn't really tell you if it starts from \(a_0\) (i.e. from n=0), OR from \(a_1\) (i.e. from n=1). So, the only thing you can say for sure that it can't be option B (\(a_{-n}\) doesn't exist).
SolomonZelman
  • SolomonZelman
basically, there is a lack of information here, without which I can't say anything.... I would assume though that they want you to say option C intuitively
anonymous
  • anonymous
Thanks !
anonymous
  • anonymous
Can you help me with the next question I have to do: What is the 9th term of the geometric sequence 4, -20, 100, …?
SolomonZelman
  • SolomonZelman
because they are proposing a thought that: "You can have first term, second term, third term, etc... something that is real (or tangible), BUT not zeroth term and certainly not negative term."
anonymous
  • anonymous
These are the options: -312,500 -12,500 62,500 1,562,500
SolomonZelman
  • SolomonZelman
ok, so it starts from \(a_1=4\) Can you find the geometric ratio for me? (if not say idk, and I will guide you through this step)
anonymous
  • anonymous
idk
SolomonZelman
  • SolomonZelman
Ok, a geometric ratio (r) in a sequence can be found using the following formula. \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{n}}{a_{n-1}}}\) where \(\large\color{black}{ \displaystyle a_{n}}\) is any term in a sequence, and \(\color{black}{\large a_{n-1}}\) is the term right before this \(\large\color{black}{ \displaystyle a_n}\). and "r" here, is of course the common ratio. ------------------ Btw, to make sure. Common ratrio is a number by which you multiply every/each time to obtain the nex term.
SolomonZelman
  • SolomonZelman
For example \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{2}}{a_1}}\) or \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{3}}{a_2}}\) or \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{4}}{a_3}}\) and on.... see?
anonymous
  • anonymous
Yes
SolomonZelman
  • SolomonZelman
now, how would you use the formula: \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{n-1}}{a_n}}\) ? Which terms would you choose? (to answer my question consider the given information - which terms do you know already?)
anonymous
  • anonymous
the common ratio is -.2 right?
SolomonZelman
  • SolomonZelman
oh, my fault
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{n}}{a_{n-1}}}\) this si the formula
SolomonZelman
  • SolomonZelman
I made a typo in my previous reply, but the rest of information is right
anonymous
  • anonymous
Is r=-.2 right?
SolomonZelman
  • SolomonZelman
so, for example \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{2}}{a_1}~~~~~\Rightarrow {\small \rm (in~this~case)~}~~~~ {\rm r}=\frac{-20}{4}=?~~~{\small \rm (you~tell~me)}}\)
SolomonZelman
  • SolomonZelman
lost?
anonymous
  • anonymous
oh I get it
SolomonZelman
  • SolomonZelman
yes, so r=?
anonymous
  • anonymous
r=-5
SolomonZelman
  • SolomonZelman
yes, r=-5. ``` Side Note: Sometimes I will be typing stuff while you are typing, and if that is the case don't be afraid to interrupt... keep typing:) ```
SolomonZelman
  • SolomonZelman
Ok, have you ever seen a formula \(\large\color{blue}{ \displaystyle a_n=a_1 \cdot {\rm r}^{n-1}}\) ?
anonymous
  • anonymous
no
SolomonZelman
  • SolomonZelman
ok, w will show what it i and how it works (if you don't mind)
SolomonZelman
  • SolomonZelman
in GEOMETRIC sequence: in order to obtain \(a_2\) you have to multiply \(a_1\) times the common ratio r. That is: \(a_1 \times {\rm r} = a_2\) correct?

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