Question

\[2a_{n-1}-a _{n-2}=3n\] in recurreance relation .. how?????

Answer 1

ok; what is the question?

Answer 2

that equ is equal to 3n .. how it is equal to 3n?? that is my question

Answer 3

well, lets see if we can algebrate it :)

Answer 4

-A{n-2} = -2A{n-1} +3n ; *-1

A{n-2} = 2A{n-1} - 3n for starters ... right?

Answer 5

but perhaps the n-1 should ne out front...

Answer 6

see this if u could get anything for this
question = 2(3(n – 1)) – 3(n – 2) = 3n = an.

Answer 7

2A{n-1} = A{n-2} + 3n /2

A{n-1} = (1/2) A{n-2} + 3n/2

Answer 8

if we add 1 to all the nth terms we get:

A{n} = (1/2) A{n-1} +3(n+1)/2

Answer 9

and you say the goal is to get to the recursive equation right?

Answer 10

i dont understand this part:

"see this if u could get anything for this question = 2(3(n – 1)) – 3(n – 2) = 3n = an."

Answer 11

ya actually the left side equation was translated to right side 3n in an recurreance solving ................

Answer 12

i too actually dont understand anything from that... the question means the equ on left on side since i need to type in equation editor i typed just as question .

Answer 13

is there a bigger qquestion that this problem comes form? it feels like I am trying to get into it halfway thru.

Answer 14

no no. not like that

Answer 15

it is starting only

Answer 16

wait i will try to google and find anything i can ..

Answer 17

well, from what you gave me; this is the most sense I can derive from it :)

Answer 18

A{n} = (1/2) A{n-1} +3(n+1)/2

Answer 19

wait i will send u the link of that ppt

Answer 20

ok :)

Answer 21

this is that ppt
see in it

Answer 22

in slide 4

Answer 23

i see it; let me read it and see what I can glean :)

Answer 24

kkkk. waiting for ur reply....

Answer 25

the first step should be to render a table of values to compare to; right? use the recurence equation to establish the data .... is my first thought

Answer 26

k..

Answer 27

if no initial conditions are specified; then a recurrence relation can have multiple solutions; becasue there is no parameters to anchor them to a specific point

Answer 28

table of values in the sense it must be its initial values??

Answer 29

if we had initial values; then we could construct a table to match the data to; yes

Answer 30

suppose I give you an equation like this:

y = 2x + d

would you be able to graph it?

Answer 31

ya

Answer 32

how? since the y intercept is a variable, where are you gonna put it on the graph?

Answer 33

since it is a recurreance relation they solve it by backward substitution method

Answer 34

the point they are making in slide 4 is that without initial values; there are many solutions that may exist.

Answer 35

A{n} = 3n is a possiblility;

so is A{n} = 5

Answer 36

the relation simply states that there is a potential family relations that exhibit the same structure; but differ only by parameters

Answer 37

just as the line y = 2x + d can have many solutions; it all depends on the value of the y intercept 'd'.

Answer 38

actually there may be many values. but how that left side = right side eqn .

get to this link and see page 2 in that pdf how they have solved that recurreance using backward substitution .

http://www.cse.unl.edu/~choueiry/S11-235/files/recitation16.pdf

i think we need to do like that to solve left side eqn to bring to right side eqn

Answer 39

i need to know how they figured out right side eqn from left side eqn??

Answer 40

by that method can u solve the above eqn on left side and bring it on right side

Answer 41

well, they didnt really solve it in slide 4; they just determined that #n was a possible solution right? and let me go over it again to make sure im on the same page as them...

Answer 42

have u seen the pdf ??

Answer 43

well, yeah, but only if you establish an initial condition; otherwise any A{0} will work

Answer 44

i saw the pdf, ive even gone thru some of these things before :)

Answer 45

working backwards you can establish a recurrence equation to determine any nth value and so on

Answer 46

oh that right. how to establish in the above question and bring 3n??

Answer 47

A{n} = 2A{n-1} – A{n-2} ; n = 2, 3, 4, …

Is A{n} = 3n a solution?

2A{n-1} – A{n-2} ; insert '3(n)' and solve

2 ( 3(n – 1)) – 3(n – 2) ; for n=2, 3(2)

2(3(1)) - 3(0) = 3(2)

2(3) - 0 = 3(2)

2(3) = 3(2) right?

Answer 48

when n = 3 does it work?

2 ( 3(n – 1)) – 3(n – 2) ; for n=3, 3(3)

2(3(2)) - 3(1) = 3(3)

2(6) - 3 = 3(3)

12 - 3 = 3(3) right?

Answer 49

Is 3n a solution to the relation? It can be, and it is valid

Answer 50

ya thanks.............

Answer 51

We can replace A{n} by 3n and have a valid solution

Answer 52

slide 3 states what I said ;)

Answer 53

since we know 3n is the answer we could substitute and prove??
if we have not known how would we have finded the 3n?? that is my question

Answer 54

'3n' only works because we have no 'initial conditions' in place.

Answer 55

slide 5 proves that A{n} = 5 is just as valid a solution

Answer 56

if we have no initial cnd then we have multiple solution?? right that is what written in slide

Answer 57

that is correct; without knowing where to start from; its impossible to get back there again

Answer 58

right. are u having any material for studying recurreance relation from basic????

Answer 59

just whats in the college library over here; oh..and I found a real good teacher online... videos actually. arsdigita, google video arsdigita

Answer 60

to make a point, all these curves have the same equation except for a y intercept to anchor them. without knowing that initial condition, which graph is the right one?

Answer 61

http://www.google.com/search?q=arsdigita&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-GB:official&client=firefox-a#q=arsdigita&oe=utf-8&rls=org.mozilla:en-GB:official&client=firefox-a&um=1&ie=UTF-8&tbo=u&tbm=vid&source=og&sa=N&hl=en&tab=wv&bav=on.2,or.r_gc.r_pw.&fp=c5bc7f2b2c3c6c4c&biw=1024&bih=629

hope this links right :)

Answer 62

ya . correct got your point..... thanks. i will see arsdigita videos.. some other materials
??

Answer 63

it chopped it .... paste that whole thing in your address bar for the videos

Answer 64

ya thanks... recurrence comes in discrete mathematics????

Answer 65

recurrence is alot of discrete math yes :)