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

- anonymous

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

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- anonymous

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

- anonymous

@ganeshie8

- anonymous

@pooja195

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## More answers

- anonymous

@perl

- pooja195

@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

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

Is it all integers?

- SolomonZelman

Can you have \(\large a_{-1}\) ??

- anonymous

they are positive

- SolomonZelman

yes, all positive integers, correct...

- anonymous

So its C?

- SolomonZelman

So your answer choice is c, n≥1.

- anonymous

Thanks!

- SolomonZelman

Also I can teach you how to put up ≥ ≤ ∞ and other symbols without copy pasting, want to know how?

- SolomonZelman

it works on almost every site...

- 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

Is an arithmetic sequence always positive integers?

- 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

Now as far as your question....

- 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

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

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

Thanks !

- 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

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

These are the options:
-312,500
-12,500
62,500
1,562,500

- 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

idk

- 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

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

Yes

- 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

the common ratio is -.2 right?

- SolomonZelman

oh, my fault

- SolomonZelman

\(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{n}}{a_{n-1}}}\)
this si the formula

- SolomonZelman

I made a typo in my previous reply, but the rest of information is right

- anonymous

Is r=-.2 right?

- 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

lost?

- anonymous

oh I get it

- SolomonZelman

yes, so r=?

- anonymous

r=-5

- 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

Ok, have you ever seen a formula \(\large\color{blue}{ \displaystyle a_n=a_1 \cdot {\rm r}^{n-1}}\) ?

- anonymous

no

- SolomonZelman

ok, w will show what it i and how it works (if you don't mind)

- 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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