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anonymous

  • one year ago

use the formula to evaluate the series 3-9+27-81+...-a8

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  1. jim_thompson5910
    • one year ago
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    post the screenshot please

  2. triciaal
    • one year ago
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    there are 2 types of series arithmetic which has a common difference from one term to the next and the geometric progression that has a common ratio from on term to the next. can you now identify what kind of series this is?

  3. anonymous
    • one year ago
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    i dont know how to do screen shot

  4. anonymous
    • one year ago
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  5. jim_thompson5910
    • one year ago
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    thanks

  6. anonymous
    • one year ago
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    okay now i know

  7. jim_thompson5910
    • one year ago
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    each term is found by multiplying the previous term by -3

  8. jim_thompson5910
    • one year ago
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    3*(-3) = -9 -9*(-3) = 27 27*(-3) = -81 etc etc

  9. anonymous
    • one year ago
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    yeah

  10. jim_thompson5910
    • one year ago
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    generate the first 8 terms, then add them up

  11. anonymous
    • one year ago
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    okay hold on lets see

  12. anonymous
    • one year ago
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    -4920

  13. jim_thompson5910
    • one year ago
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    alternatively, you can use this formula \[\Large S_n = a*\frac{1-r^n}{1-r}\]

  14. anonymous
    • one year ago
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    yeah thats what its says to use

  15. jim_thompson5910
    • one year ago
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    yeah it's -4920

  16. anonymous
    • one year ago
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    okay lets see ill send you a screen shot if its wrong okay

  17. anonymous
    • one year ago
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    you are amazing

  18. jim_thompson5910
    • one year ago
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    ok I'm glad that one worked

  19. anonymous
    • one year ago
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    okay i have another

  20. anonymous
    • one year ago
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    i have a question are you a teacher for algebra

  21. anonymous
    • one year ago
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    because you seem to know what your doing

  22. jim_thompson5910
    • one year ago
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    yes I've had lots and lots of practice

  23. anonymous
    • one year ago
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    sweet heres the other question

  24. anonymous
    • one year ago
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    1 Attachment
  25. jim_thompson5910
    • one year ago
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    this is a geometric series what's the first term? common ratio?

  26. anonymous
    • one year ago
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    1/3

  27. jim_thompson5910
    • one year ago
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    first term = 1/3, yes

  28. anonymous
    • one year ago
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    its going up in numerator x2 denomanator x3

  29. jim_thompson5910
    • one year ago
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    common ratio = -2/3

  30. anonymous
    • one year ago
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    okay

  31. anonymous
    • one year ago
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    so its diverge

  32. anonymous
    • one year ago
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    right

  33. jim_thompson5910
    • one year ago
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    r = -2/3 since |r| < 1 is true, this means the infinite series does converge and there is a fixed sum it reaches that sum would be S = a/(1-r) S = (1/3)/(1-(-2/3)) S = (1/3)/(5/3) S = (1/3)*(3/5) S = 1/5

  34. jim_thompson5910
    • one year ago
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    Rule: if |r| < 1, then the series converges otherwise, the series diverges

  35. anonymous
    • one year ago
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    okay so its fixed sum is 1/5

  36. jim_thompson5910
    • one year ago
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    if you generated all of the terms and added them up, they would add up to 1/5

  37. anonymous
    • one year ago
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    okay

  38. anonymous
    • one year ago
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    so converges are out right

  39. jim_thompson5910
    • one year ago
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    what do you mean? I wrote above that the series converges

  40. jim_thompson5910
    • one year ago
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    since |r|<1

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