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anonymous

  • one year ago

Write a formula for the general term (the nth term) of the geometric sequence. 1/2 -1/10 1/50 -1/250

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  1. anonymous
    • one year ago
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    @phi @welshfella

  2. anonymous
    • one year ago
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    A. an = 1/2(n-1)3/5 B. an = 1/2 - 1/5(n-1) C. an = (1/2)(-1/5)(n-1) D. an = (1/5)(-1/2)(n-1)

  3. phi
    • one year ago
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    any idea how to "get" from 1/2 to -1/10 ? what do you multiply 1/2 by to get -1/10 ?

  4. anonymous
    • one year ago
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    5 maybe

  5. phi
    • one year ago
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    right track. but you can do better \[ \frac{1}{2} \cdot x =- \frac{1}{10} \]

  6. phi
    • one year ago
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    if you multiply by 5 you get \[ \frac{5}{2} \] not what we want

  7. anonymous
    • one year ago
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    1/5

  8. phi
    • one year ago
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    if you can't see it, try multiplying both sides by 2 and "solve for x" 1/5 is pretty good, but not quite \[ \frac{1}{2} \cdot \frac{1}{5}= \frac{1}{10} \] but we want \[ - \frac{1}{10} \]

  9. anonymous
    • one year ago
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    so -1/5

  10. phi
    • one year ago
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    ok, and to make sure take the 2nd term in the series -1/10 and multiply by -1/5 what do we get ?

  11. anonymous
    • one year ago
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    1/15

  12. anonymous
    • one year ago
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    i think

  13. phi
    • one year ago
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    multiply top times top and bottom times bottom

  14. anonymous
    • one year ago
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    ok so 1/50

  15. phi
    • one year ago
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    and if we multiply 1/50 by -1/5 we get -1/250 notice we are getting the original series 1/2 -1/10 1/50 -1/250

  16. anonymous
    • one year ago
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    yes

  17. phi
    • one year ago
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    here is what we know \[ \frac{1}{2} \\ \frac{1}{2}\left(-\frac{1}{5}\right)^1 \\ \frac{1}{2}\left(-\frac{1}{5}\right)^2 \] and so on

  18. anonymous
    • one year ago
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    yes

  19. phi
    • one year ago
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    if we label the first term as "term number 1" and the 2nd 2 and then 3 etc notice each term has 1/2 times (-1/5) to a power one less than the term's number

  20. anonymous
    • one year ago
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    yes that makes sence

  21. phi
    • one year ago
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    only one of the choices is "short-hand" for that

  22. anonymous
    • one year ago
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    c

  23. phi
    • one year ago
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    yes

  24. anonymous
    • one year ago
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    yeah thnx again freind

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