anonymous
  • anonymous
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]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
5, -5, 5, -5, 5
anonymous
  • anonymous
SO its a geometric equation I need
anonymous
  • anonymous
the n th term is (-1)^(n+1) * 5

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anonymous
  • anonymous
the sequence would be f(n) = 5*(-1)^(n+1)
anonymous
  • anonymous
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)
anonymous
  • anonymous
the last one. (-1)^(n+1) = (-1)^(n-1)
anonymous
  • anonymous
oh ok I see now thanks:)
anonymous
  • anonymous
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
anonymous
  • anonymous
Ratio test shows that it converges. I cannot recall how to find what it converges to however.
anonymous
  • anonymous
oh ok thanks...
anonymous
  • anonymous
This is a geometric series with a = -1/4 and r = -1/4, after you factor the 2 out
anonymous
  • anonymous
So the answer is E
anonymous
  • anonymous
The infinite sum for a geometric series is a/(1-r) provided |r| < 1
anonymous
  • anonymous
oh ok so I would just plug those in and get my answer! Thanks so much!
anonymous
  • anonymous
you're welcome

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