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anonymous

  • one year ago

Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67

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  1. anonymous
    • one year ago
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    @IrishBoy123

  2. IrishBoy123
    • one year ago
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    this one is arithmetic, right? so what is the common difference?

  3. anonymous
    • one year ago
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    5

  4. IrishBoy123
    • one year ago
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    yes so \(a_1 = -8\) \(a_2 = -8 + 1(5)\) \(a_3 = -8 + 2(5)\) we will want a general term for \(a_n\), the nth term in this sequence

  5. IrishBoy123
    • one year ago
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    can you have a go at that?

  6. IrishBoy123
    • one year ago
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    |dw:1438707453164:dw|

  7. anonymous
    • one year ago
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    Would it be:\[\sum_{n=0}^{\infty}(-8+5n) \]

  8. anonymous
    • one year ago
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    @IrishBoy123

  9. IrishBoy123
    • one year ago
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    if we are starting at n = 1, you need a small tweak

  10. IrishBoy123
    • one year ago
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    if term 1 is \(a_1\), with \(n = 1\)

  11. anonymous
    • one year ago
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    sum_{n=0}^{15}(-8+5n) ?

  12. anonymous
    • one year ago
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    \[\sum_{n=0}^{15}(-8+5n)\]

  13. IrishBoy123
    • one year ago
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    \(a_1=−8 = -8 +5(1-1)\) \(a_2=−8+(5)(2-1)\) \(a_3=−8+(5)(3-1)\)

  14. IrishBoy123
    • one year ago
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    \(a_n = ??\)

  15. anonymous
    • one year ago
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    -8+5n

  16. IrishBoy123
    • one year ago
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    -8+5(n - ??)

  17. anonymous
    • one year ago
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    That's not an answer choice though. These are my answer choices: A. \[\sum_{n=0}^{15}(-8+5n)\] B. \[\sum_{n=0}^{\infty}(-40n)\] C.\[\sum_{n-0}^{15}(-40n)\] D. \[\sum_{n=0}^{\infty}(-8+5n)\]

  18. IrishBoy123
    • one year ago
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    OK, they're doing it that way, with the first term as \(a_0\) not \(a_1\) in which case you go with your suggestion, \(-8+5n\) and checking the value of \(n\) for the last term: \(-8+5n = 67 \implies n = 15\)

  19. anonymous
    • one year ago
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    Ok thanks! So it would be A?

  20. IrishBoy123
    • one year ago
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    \( \huge \checkmark \)

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