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anonymous

  • one year ago

Does anyone know how to do this Sigma Notation question?

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  1. anonymous
    • one year ago
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    This

  2. SolomonZelman
    • one year ago
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    ok. your common ratio (r) is? your first term (\(a_1\)) is? your number of terms (n) is?

  3. anonymous
    • one year ago
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    I have absolutely no clue how to figure out those thing my teacher never taught me

  4. anonymous
    • one year ago
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    @SolomonZelman

  5. SolomonZelman
    • one year ago
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    So you can't answer any of the questions I asked?

  6. anonymous
    • one year ago
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    No :(

  7. SolomonZelman
    • one year ago
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    what is this: \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=1?

  8. anonymous
    • one year ago
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    -2?

  9. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=1: \(\large\color{black}{ \displaystyle2(-2)^{1-1} =2(-2)^0=2\cdot 1=2}\)

  10. SolomonZelman
    • one year ago
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    Ok, can you tell me what is \(\large\color{black}{ \displaystyle 2(-2)^{n-1} }\) when n=2?

  11. SolomonZelman
    • one year ago
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    plug in 2 instead of n....

  12. anonymous
    • one year ago
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    -4?

  13. anonymous
    • one year ago
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    @SolomonZelman

  14. SolomonZelman
    • one year ago
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    yes

  15. SolomonZelman
    • one year ago
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    ok, now do the same when n=3

  16. anonymous
    • one year ago
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    8

  17. SolomonZelman
    • one year ago
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    yes.

  18. SolomonZelman
    • one year ago
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    So so frar your terms are: 2, -4, 8.... do you notice any pattern?

  19. SolomonZelman
    • one year ago
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    you multiply times -2 every time, is this correct?

  20. anonymous
    • one year ago
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    yes'

  21. SolomonZelman
    • one year ago
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    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.

  22. SolomonZelman
    • one year ago
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    So, we can say that r=-2

  23. SolomonZelman
    • one year ago
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    Now, what does your sequence start from, what is the first term?

  24. anonymous
    • one year ago
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    2

  25. SolomonZelman
    • one year ago
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    yes

  26. SolomonZelman
    • one year ago
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    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 \(a_n\) -----------------------------

  27. SolomonZelman
    • one year ago
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    And then your number of terms is 7 (i colored it in blue) \(\Large\color{black}{ \displaystyle \sum_{ n=1 }^{\color{blue}{7}} 2(-2)^{n-1} }\)

  28. SolomonZelman
    • one year ago
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    so, now, again, pliz answer my 3 questions that I asked in the very beginning.

  29. anonymous
    • one year ago
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    your common ratio (r) is? -2 your first term (a1) is? 2 your number of terms (n) is? 7

  30. anonymous
    • one year ago
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    @SolomonZelman

  31. freckles
    • one year ago
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    do you still need help on this ?

  32. freckles
    • one year ago
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    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

  33. SolomonZelman
    • one year ago
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    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!

  34. SolomonZelman
    • one year ago
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    and the answers to my initial 3 questions are correct, good job.

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