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Cutiepo0
Group Title
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 :)
 2 years ago
 2 years ago
Cutiepo0 Group Title
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 :)
 2 years ago
 2 years ago

This Question is Closed

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339363260817:dw
 2 years ago

asnaseer Group TitleBest 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/
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339363321532:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
your answers are not correct
 2 years ago

Cutiepo0 Group TitleBest ResponseYou've already chosen the best response.0
yeah I just realized that
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
yes  the equation I ended up with agrees with the values found by mahmit2012
 2 years ago

asnaseer Group TitleBest 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?
 2 years ago

Cutiepo0 Group TitleBest 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
 2 years ago

asnaseer Group TitleBest 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
 2 years ago

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

Cutiepo0 Group TitleBest 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 :$
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
your formula does not produce the right answers
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
take n=1  it produces the value 3
 2 years ago

Cutiepo0 Group TitleBest ResponseYou've already chosen the best response.0
yeah I just checked, you're right it gave me the wrong answer.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
if you use the formula I derived then it matches all the values (listed by mahmit2012)
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
I can try and explain the steps I took to derive this
 2 years ago

Cutiepo0 Group TitleBest ResponseYou've already chosen the best response.0
okay, thanks that would be good
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339364532207:dw
 2 years ago

asnaseer Group TitleBest 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.
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339364595544:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339364644950:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339364681732:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339364741953:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1339364774607:dw
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
hope it all makes sense?
 2 years ago

Cutiepo0 Group TitleBest ResponseYou've already chosen the best response.0
thanks a lot guys :)
 2 years ago
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