anonymous
  • anonymous
Calculus Problem!! Suppose you figure out that if you oversleep one night, you undersleep the following night, and vice-versa. The pattern follows xn+1 = (1/2)(xn + xn+1), where x0 = 7 and x1 = 6 are the hours of sleep you get in the first two nights. What is the explicit formula?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[x _{n+1} = (1/2)(x _{n} + x _{n+1}), where x _{0} = 7 and x _{1} = 6\]
experimentX
  • experimentX
for even: x(2n) = x(2n-2) for odd: x(2n+1) = x(2n-1)
anonymous
  • anonymous
i have to express it as \[X _{n}=\]

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experimentX
  • experimentX
x(n) = x(n-2) .. i suppose
anonymous
  • anonymous
\[X _{0}=7,X _{1}=6,X _{2}=6.5,X _{3}=6.25,X _{4}=6.375,X _{5}=6.3125,X _{6}=6.34375\]
experimentX
  • experimentX
x(n+2) = 1/2 (x(n)+x(n+1))
TuringTest
  • TuringTest
by "explicit formula" do you mean solve for \(x_n\) ?
anonymous
  • anonymous
yea,i think so.\[X _{n}=\]...n and make this formula works for all the terms\[X _{0},X _{1}\]etc.
dumbcow
  • dumbcow
the limit of x_n as n-> infinity is 19/3 it alternates above and below this value \[\rightarrow X_{n} = \frac{19}{3}+\frac{(-1)^{n}}{3*2^{n-1}}\]
anonymous
  • anonymous
@dumbcow Thank you so much!! @TuringTest @experimentX Thanks for your time too!!
TuringTest
  • TuringTest
I didn't even do anything :P
anonymous
  • anonymous
at least you looked at it,hehe^^

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