Re: need help evaluating a recursuive sequence on ti 86!!!!!!!!
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Re: need help evaluating a recursuive sequence on ti 86!!!!!!!!
On Thu, 17 Dec 1998 07:01:40 GMT, "Ax-Man" <krw699@aol.com> wrote:
>Can anybody tell me how to evaluate a recursively defined sequence.
>
>a(1) = 2
>a(n) = a(n-1) + (4/a(n-1))
>
>I have a ti 86 and cannot find out how to do this. my friends are able to
>do it on their 82's and 85's but I cant. I need to evaluate it from
>1000-1009.
>
>Help
>
>Ken
Hi,
I don't know about the TI-86 but
the TI-85 cannot do true recursion and anyway
recursion is slower most of the time. Imagine this : the
program must first display the point for Fn(1000). To do this
it must compute all intermediates results from Fn(2) to Fn(999).
Next, it must display the point for Fn(1001) but to do that it
must recompute all intermediates results again and then add the
last value!
All recursive functions can be turned into iterative functions.
In BASIC, your function look like:
Answer=2
FOR i = 2 to 1010
Answer = Answer + Answer / 4
NEXT i
print Answer
You wrote in another message that you want to plot the function.
I have included here 2 programs written for the TI-85 for that.
It shoulb be similar for the TI-86. The first one
will plot only the values from 1000 to 1009 and it will
store then in the list LY. Notice that it must compute all
preceding values anyway, that is why there is 2 "for" loops.
I have listed these values at the end of this text.
The second one will plot all values from 2 to 1010.
{^;^}
/ \ Benont Morrissette, remove "NOSPAM" in adress to reply
personnaly
Note: In the listings below, the key STO> is shown as ->
with spaces on either side.
-----------------start of RECURS1-----------------------
PROGRAM:RECURS1
:FnOff
:ClDrw
:999 -> xMin
:1010 -> xMax
:1 -> xScl
:89 -> yMin
:91 -> yMax
:.1 -> yScl
:10 -> dimL LX
:10 -> dimL LY
:2 -> REP
:1 -> IND
:For(i,2,999)
:REP+4/REP -> REP
:End
:For(i,1000,1009)
:REP+4/REP -> REP
:i -> LX(IND)
:REP -> LY(IND)
:IND+1 -> IND
:End
:xyLine LX,LY
-------------------end of RECURS1-----------------------
execution time : 9 seconds.
-----------------start of RECURS2-----------------------
PROGRAM:RECURS2
:FnOff
:ClDrw
:0 -> xMin
:1010 -> xMax
:100 -> xScl
:0 -> yMin
:91 -> yMax
:10 -> yScl
:2 -> REP
:For(i,2,1010)
:REP+4/REP -> REP
:PtOn(i,REP)
:End
-------------------end of RECURS2-----------------------
execution time : 15 seconds.
1000 89.51374618411995
1001 89.55843205830706
1002 89.6030956361307
1003 89.647736950938
1004 89.69235603599297
1005 89.73695292447692
1006 89.78152764948867
1007 89.82608024404482
1008 89.87061074108011
1009 89.91511917344766
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