A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Write an explicit formula for the sequence determined by the recursion formula tn=(0.5tn1)+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 :)
anonymous
 4 years ago
Write an explicit formula for the sequence determined by the recursion formula tn=(0.5tn1)+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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is it t_n=.5t_n1+1 or t_n=t_n1+n?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so it would probobly help if we plug in some values: we know that .5=1/2 so with this we can work easier. t1=40=t0/2+1 so t0=78 now let's plug in some values for n: t1=t0/2+1 t2=t1/2+2=(t0/2+1)/2+2=t0/4+1/2+2 t3=t2/2+3=(t0/4+1/2+2)/2+3=t0/8+1/4+4 t4=t3/2+4=(t0/8+1/4+4)/2+4=t0/16+1/8+6 t5=t4/2+5=(t0/16+1/8+6)/2+5=t0/32+1/18+8 now as you can see, the first term seems to have pattern t0/2^n. the second term seems to have pattern 1/2^{n1} and the third is just a sequence of even numbers which starts with 0 so the formula for that third term will be 2n2. so we have: tn=t0/2^n+1/2^{n1}+2n2 now since t0=78, tn then becomes: tn=(78/2^n)+(1/2^{n1})+(2n2) rechecking, you'll see that using this formula will also give t1=40, t2=22, t3=13, t4 = 8.5, t5=6.25
Ask your own question
Sign UpFind 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.