Given the geometric sequence where a1 = -3 and the common ratio is 9, what is the domain for n?

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Given the geometric sequence where a1 = -3 and the common ratio is 9, what is the domain for n?

Mathematics
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OPTIONS All integers All integers where n ≥ -1 All integers where n ≥ 1 All integers where n ≥ 0

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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).
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 ?
Is it all integers?
Can you have \(\large a_{-1}\) ??
they are positive
yes, all positive integers, correct...
So its C?
So your answer choice is c, n≥1.
Thanks!
Also I can teach you how to put up ≥ ≤ ∞ and other symbols without copy pasting, want to know how?
it works on almost every site...
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
Is an arithmetic sequence always positive integers?
\(\large\color{blue}{ \displaystyle {\rm CODES,~~short~guide} }\) 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 `
Now as far as your question....
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 \(\large\color{black}{ \displaystyle a_n=-3+9(n-1) }\)
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).
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
Thanks !
Can you help me with the next question I have to do: What is the 9th term of the geometric sequence 4, -20, 100, …?
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."
These are the options: -312,500 -12,500 62,500 1,562,500
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)
idk
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.
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?
Yes
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?)
the common ratio is -.2 right?
oh, my fault
\(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{n}}{a_{n-1}}}\) this si the formula
I made a typo in my previous reply, but the rest of information is right
Is r=-.2 right?
so, for example \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{2}}{a_1}~~~~~\Rightarrow {\small \rm (in~this~case)~}~~~~ {\rm r}=\frac{-20}{4}=?~~~{\small \rm (you~tell~me)}}\)
lost?
oh I get it
yes, so r=?
r=-5
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:) ```
Ok, have you ever seen a formula \(\large\color{blue}{ \displaystyle a_n=a_1 \cdot {\rm r}^{n-1}}\) ?
no
ok, w will show what it i and how it works (if you don't mind)
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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