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Life

  • 2 years ago

Write each arithmetic series as the sum of terms, find each sum.

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  1. Life
    • 2 years ago
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    |dw:1354173691072:dw|

  2. Life
    • 2 years ago
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    this one's different

  3. Life
    • 2 years ago
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    how do i find a_1

  4. Life
    • 2 years ago
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    is it -5?

  5. sagarrobo
    • 2 years ago
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    |dw:1354173877445:dw| put k=10 and get answer

  6. sagarrobo
    • 2 years ago
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    answer=1000-275=725

  7. Life
    • 2 years ago
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    does a_1 =-5 ?

  8. geoffb
    • 2 years ago
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    \(a_1\) is the result of the equation when you plug your first term into it. Your equation is \(100-5k\). The series starts when k = 1, so plug 1 in for k and solve. That's \(a_1\).

  9. sagarrobo
    • 2 years ago
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    100-5k is general term for k series so first term=95

  10. Life
    • 2 years ago
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    what about a_n, |dw:1354174176642:dw|

  11. Life
    • 2 years ago
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    its wrong i know...

  12. sagarrobo
    • 2 years ago
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    its wrong refer to my solution above in figure

  13. geoffb
    • 2 years ago
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    @Life: You need to distinguish between the formula for the sum of the series and the equation you're given (in this case, 100-5k). You need to find the value for \(a_{10}\), and then plug that into your series summation formula.

  14. geoffb
    • 2 years ago
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    \(a_1 = 95\) (you solved that already). \(a_{n} = a_{10} = 100-5(10)\) Plug \(a_{1}\), \(a_{10}\) (which is the *value* you get—*not* 10), and \(n\) into your \(S_{n}\) formula and solve.

  15. Life
    • 2 years ago
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    i dont understand how "I" got 95, i never did, but i undetstand everything after that, i thought a1=-5

  16. geoffb
    • 2 years ago
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    Your equation is \(100-5k\), so \(a_{1}\) will be the result you get when you plug 1 in for \(k\).

  17. geoffb
    • 2 years ago
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    \(a_{2}\) will be the result you get when you plug in 2 for \(k\). \(a_{3}\) will be the result you get when you plug in 3 for \(k\). ... \(a_{10}\) will be the result you get when you plug in 10 for \(k\).

  18. geoffb
    • 2 years ago
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    @Life: Have you ever done computer programming? If so, do you know what a for loop is?

  19. geoffb
    • 2 years ago
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    That's all a series is. For each value from what's below sigma to what's above it (in this case, between k=1 and k=10), perform the equation. Once you know each one, add them all together.

  20. Life
    • 2 years ago
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    my final answer, s10=725, AM I RIGHT? :)

  21. geoffb
    • 2 years ago
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    Yes.

  22. Life
    • 2 years ago
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    sorry for being dumb lol, i understand it now though, so it was all worth it

  23. geoffb
    • 2 years ago
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    You're not being dumb. You are showing effort (not just "what's the answer?"), which is appreciated. :)

  24. geoffb
    • 2 years ago
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    Good luck with the rest of them. I have faith that you'll get them all. Good night. :)

  25. Life
    • 2 years ago
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    Good night :D

  26. Life
    • 2 years ago
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    I really do appreciate you sticking with me until i understood it. It was probably a good half an hour before I finally understood it, so thanks a bunch

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