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anonymous

  • one year ago

write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 +...+67 @ganeshie8 @dan815 @michele_Laino @nincompoop @solomonzelman @ paki @nnesha @undeadknight26

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  1. Michele_Laino
    • one year ago
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    it is an arithmetic sequence, the first term is -8, whereas the last term is 67, furthermore, the constant of the sequence is: -3-(-8)=2-(-3)=...? please complete

  2. anonymous
    • one year ago
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    5 @Michele_Laino

  3. Michele_Laino
    • one year ago
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    that's right!

  4. Michele_Laino
    • one year ago
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    now, we have to know how many terms are into your sequence. In order to do that, we have to use this general formula: \[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]

  5. Michele_Laino
    • one year ago
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    where n is the number of terms, d=5, a_1=-8, and a_n=67

  6. Michele_Laino
    • one year ago
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    substituting those quantities, we can write: \[67 = - 8 + \left( {n - 1} \right) \times 5\]

  7. Michele_Laino
    • one year ago
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    what is n?

  8. anonymous
    • one year ago
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    16?

  9. Michele_Laino
    • one year ago
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    that's right! we have n= 16 terms in our sequence

  10. Michele_Laino
    • one year ago
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    so the requested sum S is given by the subsequent formula: \[S = \frac{{{a_1} + {a_n}}}{2} \times n\]

  11. Michele_Laino
    • one year ago
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    where a_1=-8, a_n=67, n=16, please substitute into that formula above

  12. Michele_Laino
    • one year ago
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    \[S = \frac{{{a_1} + {a_n}}}{2} \times n = \frac{{ - 8 + 67}}{2} \times 16 = ...?\]

  13. anonymous
    • one year ago
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    472?

  14. Michele_Laino
    • one year ago
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    correct!

  15. anonymous
    • one year ago
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    what do i do next?

  16. Michele_Laino
    • one year ago
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    we have completed your exercise

  17. anonymous
    • one year ago
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    no i have to put it in sum notation @Michele_Laino

  18. Michele_Laino
    • one year ago
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    then I think that we have to write this: \[\begin{gathered} - 8 + \left( { - 3} \right) + 2 + 7 + 12 + 17 + + 22 + 27 + 32 + 37 + \hfill \\ + 42 + 47 + 52 + 57 + 62 + 67 = 472 \hfill \\ \end{gathered} \]

  19. Michele_Laino
    • one year ago
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    is it right?

  20. anonymous
    • one year ago
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    i need to write it in sum notation form?

  21. Michele_Laino
    • one year ago
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    sorry what do you mean with "notation form"?

  22. anonymous
    • one year ago
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    summation notation

  23. Michele_Laino
    • one year ago
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    we can write this: \[\Large \sum\limits_1^{16} { - 8 + \left( {n - 1} \right) \times 5} = 472\]

  24. Michele_Laino
    • one year ago
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    or: \[\Large \sum\limits_1^{16} {\left[ { - 8 + \left( {n - 1} \right) \times 5} \right]} = 472\]

  25. anonymous
    • one year ago
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    these are none of my options

  26. Michele_Laino
    • one year ago
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    which can be simplified as follows: \[\Large \sum\limits_1^{16} {\left( {5n - 13} \right)} = 472\]

  27. Michele_Laino
    • one year ago
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    now?

  28. anonymous
    • one year ago
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    nope

  29. Michele_Laino
    • one year ago
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    \[\Large \sum\limits_1^{16} n = 136\] now?

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