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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    OPTIONS All integers All integers where n ≥ -1 All integers where n ≥ 1 All integers where n ≥ 0

  2. anonymous
    • one year ago
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    @ganeshie8

  3. anonymous
    • one year ago
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    @pooja195

  4. anonymous
    • one year ago
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    @perl

  5. pooja195
    • one year ago
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    @SolomonZelman ;-; ?

  6. SolomonZelman
    • one year ago
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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).

  7. SolomonZelman
    • one year ago
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    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 ?

  8. anonymous
    • one year ago
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    Is it all integers?

  9. SolomonZelman
    • one year ago
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    Can you have \(\large a_{-1}\) ??

  10. anonymous
    • one year ago
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    they are positive

  11. SolomonZelman
    • one year ago
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    yes, all positive integers, correct...

  12. anonymous
    • one year ago
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    So its C?

  13. SolomonZelman
    • one year ago
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    So your answer choice is c, n≥1.

  14. anonymous
    • one year ago
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    Thanks!

  15. SolomonZelman
    • one year ago
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    Also I can teach you how to put up ≥ ≤ ∞ and other symbols without copy pasting, want to know how?

  16. SolomonZelman
    • one year ago
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    it works on almost every site...

  17. anonymous
    • one year ago
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    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

  18. anonymous
    • one year ago
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    Is an arithmetic sequence always positive integers?

  19. SolomonZelman
    • one year ago
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    \(\large\color{blue}{ \displaystyle {\rm CODES,~~short~guide} }\) 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 `

  20. SolomonZelman
    • one year ago
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    Now as far as your question....

  21. SolomonZelman
    • one year ago
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    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 \(\large\color{black}{ \displaystyle a_n=-3+9(n-1) }\)

  22. SolomonZelman
    • one year ago
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    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).

  23. SolomonZelman
    • one year ago
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    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

  24. anonymous
    • one year ago
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    Thanks !

  25. anonymous
    • one year ago
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    Can you help me with the next question I have to do: What is the 9th term of the geometric sequence 4, -20, 100, ?

  26. SolomonZelman
    • one year ago
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    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."

  27. anonymous
    • one year ago
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    These are the options: -312,500 -12,500 62,500 1,562,500

  28. SolomonZelman
    • one year ago
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    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)

  29. anonymous
    • one year ago
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    idk

  30. SolomonZelman
    • one year ago
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    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.

  31. SolomonZelman
    • one year ago
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    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?

  32. anonymous
    • one year ago
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    Yes

  33. SolomonZelman
    • one year ago
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    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?)

  34. anonymous
    • one year ago
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    the common ratio is -.2 right?

  35. SolomonZelman
    • one year ago
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    oh, my fault

  36. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{n}}{a_{n-1}}}\) this si the formula

  37. SolomonZelman
    • one year ago
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    I made a typo in my previous reply, but the rest of information is right

  38. anonymous
    • one year ago
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    Is r=-.2 right?

  39. SolomonZelman
    • one year ago
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    so, for example \(\large\color{black}{ \displaystyle {\rm r}=\frac{a_{2}}{a_1}~~~~~\Rightarrow {\small \rm (in~this~case)~}~~~~ {\rm r}=\frac{-20}{4}=?~~~{\small \rm (you~tell~me)}}\)

  40. SolomonZelman
    • one year ago
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    lost?

  41. anonymous
    • one year ago
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    oh I get it

  42. SolomonZelman
    • one year ago
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    yes, so r=?

  43. anonymous
    • one year ago
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    r=-5

  44. SolomonZelman
    • one year ago
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    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:) ```

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

  46. anonymous
    • one year ago
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    no

  47. SolomonZelman
    • one year ago
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    ok, w will show what it i and how it works (if you don't mind)

  48. SolomonZelman
    • one year ago
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    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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