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Write an explicit formula for the sequence determined by the recursion formula \[t n = 0.5t _{n1}+n\]
t1=40, t2=22, t3=13, t4 = 8.5, t5=6.25
Please explain how to get to the answer rather than just the answer. Thanks :)
 one year ago
 one year ago
Write an explicit formula for the sequence determined by the recursion formula \[t n = 0.5t _{n1}+n\] t1=40, t2=22, t3=13, t4 = 8.5, t5=6.25 Please explain how to get to the answer rather than just the answer. Thanks :)
 one year ago
 one year ago

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mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339363260817:dw
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
I used this site to help me understand how to solve this: http://hcmop.wordpress.com/2012/04/20/usingcharacteristicequationtosolvegenerallinearrecurrencerelations/
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339363321532:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
your answers are not correct
 one year ago

Cutiepo0Best ResponseYou've already chosen the best response.0
yeah I just realized that
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
yes  the equation I ended up with agrees with the values found by mahmit2012
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
I can let you know what equation I found if you want  or do you want to try it yourself first?
 one year ago

Cutiepo0Best ResponseYou've already chosen the best response.0
I know the answer, it's tn= ((n+1)(n+2))/2 but I don't know how to get to it
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
I haven't done problems like this before but found that document and followed it to get the answer
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
I actually got:\[t_n=80(\frac{1}{2})^n+2(n1)\]
 one year ago

Cutiepo0Best ResponseYou've already chosen the best response.0
yeah but the textbook gave me the answer I posted. And that website uses very complex explanations :$
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
your formula does not produce the right answers
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
take n=1  it produces the value 3
 one year ago

Cutiepo0Best ResponseYou've already chosen the best response.0
yeah I just checked, you're right it gave me the wrong answer.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
if you use the formula I derived then it matches all the values (listed by mahmit2012)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
I can try and explain the steps I took to derive this
 one year ago

Cutiepo0Best ResponseYou've already chosen the best response.0
okay, thanks that would be good
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339364532207:dw
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
ok  first it said arrange the recurrence relation in the form:\[At_n+Bt_{n1}+Ct_{n2}+...=f(n)\]so I arranged your relation as:\[t_n0.5t_{n1}=n\tag{a}\]it then said the general solution when f(n) is zero is \(t_n=A(0.5)^n\). It then said that to take account of f(n) we need to add in a solution of the form \(Bn+C\). So we substitute this into (a) to get:\[Bn+c0.5(B(n1)+C)=n\]which leads to:\[0.5Bn+0.5(B+C)=n\]and if we equate coefficients of LHS and RHS we get:\[B=2\]\[B+C=0\implies C=B=2\]so the second part of the equation is of the form:\[2n2\]we add this to the first part to get the answer:\[t_n=A(0.5)^n+2n2\]then use the fact that \(t_1=40\) to find A.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339364595544:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339364644950:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339364681732:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339364741953:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1339364774607:dw
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
hope it all makes sense?
 one year ago
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