A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Find the first four terms of a squence using the recursive definition.
f(1)=6, f(n)=f(n1)5
anonymous
 one year ago
Find the first four terms of a squence using the recursive definition. f(1)=6, f(n)=f(n1)5

This Question is Closed

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3what does the definition tell us?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Using a process that can be repeated. So like the arithmetic sequence. The arithmetic sequence is adding a constant of the previous term.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3ok, in this case, what are we 'adding' to one term to make the next term? any ideas?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3or if we simply let n={1,2,3,4} and the rule defined, we get: f(1) = 6 f(2) = f(1) 5 f(3) = f(2) 5 f(4) = f(3) 5

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3so, what would our 4 terms be?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So since its asking for the first four terms wouldnt it be f(1)=6 f(n)=f(n1)5 f(2)=f(21)5=f(1)+1= 6+1=7 so 7 would be one of the four terms but I dont know how to get the rest.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3f(2) = f(21)  5 f(2) = f(1)  5 f(2) = 6  5 = 1, not 7 so, f(1) = 6, f(2) = 1  now repeat with n=3 f(3) = f(31)  5 f(3) = f(2)  5 f(3) = 1  5 = 4 so, f(1) = 6, f(2) = 1, f(3) = 4 what is f(4) ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3as we find each new term, we can use it to find the next one .... hence the naming it: 'recursive'

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3f(4) = f(41)  5 f(4) = f(3)  5 ^^^ but we know f(3) = 1 f(4) = 1  5

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3pfft, f(3) = 4 .... these tired old eyes play tricks on me

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3can you tell me how we are working this? its basic to me so i cant really see the difficulty. you have to tell me what it is that is confusing you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oka, I understand but im confused on f(4)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3ok, tell me how you are looking at f(4) show me your working

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3if you know how to get from f(1) to f(2), then the process does not change. f(2) allows us to get f(3), and f(3) allows us to get f(4). typing errors aside, its pretty repetitive.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3f(4) = f(3)  5 f(3) = 4 [i mistyped it before as 1] f(4) = 4 5

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3another way to look at it, just subtract 5 from the setup before ... f(1) = 6 f(2) = 65 f(3) = 655 f(4) = 6555

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3now, what are our 4 terms?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3f(1) = 6 f(2) = 65 = 1 f(3) = 655 = 4 f(4) = 6555 = 9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh im sorry I didnt mean to write 5 but thank you so much

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3\[\begin{pmatrix}n\\f(n)\end{pmatrix}=\begin{pmatrix}1&2&3&4\\6&1&4&5\end{pmatrix}\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3yeah, 6, 1 4, 9 math and typing dont mix that well

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I agree on that ,Do you think you can help me with a couple more?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3maybe one more; its late (1235) and work comes early in the morning

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay thank you. f(1)=2,f(n)=3f(n1)+[f(n1)]^2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3well this ones just a exercise in plugging in the value ... show me your work for n=2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3dunno if it helps any to rewrite it by factoring: f(n) = f(n1) [f(n1) 3] your call

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait okay so do I plug 2 in for n?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3ideally yes, since 2 is the number after 1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay so I have f(2)=3f(21)+[f(21)]^2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3good, and since 21 = 1 f(2) = 3 f(1) + [f(1)]^2 and what does f(1) equal?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not sure in what to do after

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3you replace f(1) with what its vale is, and work the math

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So would Imultiply 3 by 1? =3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Or where would I get the value from?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3f(1) has been defined for you already in your setup f(1)=2 < f(n)=3f(n1)+[f(n1)]^2  f(2) = 3 f(1) + [f(1)]^2 f(2) = 3(2) + 2^2 = 6+4 = 2 f(2) = 2  we know f(2) now, so let n=3 and work the process again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay thank you so much

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3youre welcome .... once we know a new term, we can use it to find the next new term f(3) = 3 f(2) + [f(2)]^2 f(3) = 3(2) + [2]^2 = 6+4 f(3) = 10  f(4) = 3 f(3) + [f(3)]^2 f(4) = 3(10) + 10^2 = 10030 etc ....
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.