recursive sequences

[pam]

Hi group:

I know how to define a sequence recursively using a graph page. I'm wondering, though, if there is an easy way to define a sequence recursively on a calculator page. I've tried define seq( ..., but can't figure out the syntax. I tried using a template to enter two parts, but that didn't work either. I'm sure it's something quite simple. Help?

Thanks.

Pam

[John Hanna]

Re: easy way to define a sequence recursively on a calculator page

 

 

 

It could be better, I suppose, but the pool is waiting!

John Hanna

jeh...@optonline.net

www.johnhanna.us

T³ - Teachers Teaching with Technology

"A cowchip is paradise to a fly."

 

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[Wayne]

The calculator page command for defining recursive sequences is
seqn() .
Wayne

On 13 June, 15:07, pam <pamela.raw...@gmail.com> wrote:
> Hi group:
>
> I know how to define a sequence recursively using a graph page. I'm

> wondering, though, if there is an easy way to define a sequence *recursively
> * on a calculator page. I've tried define seq( ..., but can't figure out the

[Wayne]

Sorry, I forgot to add an example: for the first 10 terms of the
fibonacci sequence, seqn(u(n-1)+u(n-2),{1,1},10) .
Wayne

[pam]

That worked with the CAS unit my student has. I was even able to use the variables we've been using in class rather than generic f(x). Very cool. I figured there was a way to use piecewise functions to do this; I just couldn't figure out the syntax. 

I'm guessing that the seq function has to use an explicit formula (like on the 84) since it appears to have the same syntax.

Thanks!

Pam

[pam]

Wayne,

That helps a great deal. Too bad the CAS handheld doesn't seem to have the seqn command (although I haven't updated to OS 3 yet ... maybe it does).

Thanks!

Pam

[Nevil Hopley]

I think that all OS's since 2.0 have had the seqn command, but it
doesn't appear in the catalog for some reason, and I don't think it's
even mentioned in the pdf reference guides either.
I've not checked recently though to verify this claim of mine!

Nevil

[Wayne]

Pam and Nevil,

Yes, seqn() is new in OS 3.0 . OS 3.0 added that command as well as
seqGen(), both of which are quite useful. There were also some issues
with the way the old OS allowed sequence graphing pages to interact
with a calculator page and those have been eliminated, as far as I can
tell. One example in which seqn() provides a good classroom aid is to
quickly generate the iterates for the Newton approximation of zeros of
functions. That's a topic that is in just about every first semester
calculus class.

Wayne

On 14 June, 11:52, Nevil Hopley <ne...@calculatorsoftware.co.uk>
wrote:

[Wayne]

On a related note, OS 3.0 not only added seqn() and seqGen() but
euler() was also added to the catalog. Euler() is a function that
generates the Euler approximation sequence for a given differential
equation. Of course, it is the same sequence that is generated and
displayed in the new DE grapher in OS 3.0. Euler() is useful when
that approximation is covered in Calculus 1 or 2.

Wayne

[Jimmy Fullerenex]

Just to add, the counterpart of euler(), rk23() is also present. About the new euler() function, while it certainly provides a good build-in functionality, it also eats up my own version of "euler()" in a document (I don't even have the chance to recover it!) and so does completesquare(). But anyway, I surely appreciate TI's improvements, and I'm also keenly anticipating new CAS advanced commands.

Cheers,

Jimmy Fullerenex

2011/6/15 Wayne <wayn...@thepaces.org>