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anonymous

  • 5 years ago

Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.) a[1]=5,a[k+1]=-a[k]

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  1. anonymous
    • 5 years ago
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    5, -5, 5, -5, 5

  2. anonymous
    • 5 years ago
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    SO its a geometric equation I need

  3. anonymous
    • 5 years ago
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    the n th term is (-1)^(n+1) * 5

  4. anonymous
    • 5 years ago
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    the sequence would be f(n) = 5*(-1)^(n+1)

  5. anonymous
    • 5 years ago
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    ok well these are my options: a[n]=5n a[n]=5(-1)^n a[n]=-5^n a[n]=-5^(n-1) a[n]=5(-1)^(n-1)

  6. anonymous
    • 5 years ago
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    the last one. (-1)^(n+1) = (-1)^(n-1)

  7. anonymous
    • 5 years ago
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    oh ok I see now thanks:)

  8. anonymous
    • 5 years ago
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    Find the sum of the infinite series. \[\sum_{i=1}^{\infty}2(-1/4)^i\] A. Undefined B. -2/3 C. 2 D.4/5 E. -2/5

  9. anonymous
    • 5 years ago
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    Ratio test shows that it converges. I cannot recall how to find what it converges to however.

  10. anonymous
    • 5 years ago
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    oh ok thanks...

  11. anonymous
    • 5 years ago
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    This is a geometric series with a = -1/4 and r = -1/4, after you factor the 2 out

  12. anonymous
    • 5 years ago
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    So the answer is E

  13. anonymous
    • 5 years ago
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    The infinite sum for a geometric series is a/(1-r) provided |r| < 1

  14. anonymous
    • 5 years ago
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    oh ok so I would just plug those in and get my answer! Thanks so much!

  15. anonymous
    • 5 years ago
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    you're welcome

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