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anonymous

  • one year ago

Find s10 for -1+-7+-13+-19+...

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  1. SolomonZelman
    • one year ago
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    what pattern do you notice in this sequence?

  2. anonymous
    • one year ago
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    the r=-6

  3. SolomonZelman
    • one year ago
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    not, exactly. You go down by 6 every time (i.e. subtract 6) BUT the correct notation is d=-6

  4. SolomonZelman
    • one year ago
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    when you say d=-6 that would mean you subtract -6, if you say r=-6 that would mean you are multiplying times -6 d = common difference (adding) r = common ratio (multiplying)

  5. SolomonZelman
    • one year ago
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    You need to find the 10th term first, can you do that for me?

  6. SolomonZelman
    • one year ago
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    [[ Use \(\large a_{\rm n}=a_1+{\rm d( n}-1) \) ]]

  7. SolomonZelman
    • one year ago
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    r u lost?

  8. anonymous
    • one year ago
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    I got -55?

  9. SolomonZelman
    • one year ago
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    Oh, a(10)=-1+(-6)(10-1)=-1+(-6)(9)=-1-54=-55 correct \(a_{10}=-55\)

  10. SolomonZelman
    • one year ago
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    Now, (when you start from \(a_1\) and end the series at \(a_n\) (provided this series is arithmetic, which it is in this case) the sum, for n terms is given the following way: \(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm n} } A_{\rm n}=\color{red}{\frac{1}{2} \left(a_1+a_{\rm n}\right)}\times \color{blue}{{\rm n}} }\)

  11. SolomonZelman
    • one year ago
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    in red I labeled the part of the formula which is the average term. in blue is the number of term

  12. SolomonZelman
    • one year ago
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    number of terms*

  13. SolomonZelman
    • one year ago
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    well, I should have made the number of terms k... but I will show you how to use this. \(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm 10} } A_{\rm n}=\color{red}{\frac{1}{2} \left(-1+-55\right)}\times \color{blue}{{\rm 10}} }\)

  14. SolomonZelman
    • one year ago
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    in this case.... c y?

  15. SolomonZelman
    • one year ago
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    (if you want I can restart in a more handy way, typing isn't a problem.... )

  16. anonymous
    • one year ago
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    I got -280 is that right? @SolomonZelman

  17. SolomonZelman
    • one year ago
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    no

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is replying to Can someone tell me what button the professor is hitting...

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