A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years 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 :)
 2 years 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 :)

This Question is Closed

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

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

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

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

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

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

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

Cutiepo0
 2 years ago
Best ResponseYou've already chosen the best response.0I know the answer, it's tn= ((n+1)(n+2))/2 but I don't know how to get to it

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

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

Cutiepo0
 2 years ago
Best ResponseYou've already chosen the best response.0yeah but the textbook gave me the answer I posted. And that website uses very complex explanations :$

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

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

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

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

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

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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0ok  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.

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

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

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

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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0hope it all makes sense?
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.