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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: j23 on January 22, 2013, 10:08:04 pm

Title: sequences and series cas help !!
Post by: j23 on January 22, 2013, 10:08:04 pm: i'm having some trouble on spec essentials book chapter 1A Toolbox exercise 1E.

Does anyone have a cheat sheet or the formula to how to find a specific term number or the values within a sequence? Or even the sum of an infinite sequence? (Im using the CAS new black calc). Thanks !!
Title: Re: sequences and series cas help !!
Post by: Dr. Ban on January 24, 2013, 11:34:26 am: I feel your pain! I have the same CAS (TI -Nspire CX CAS) and when I tried to solve using the CAS nothing happened!I did for like an hour before I just gave up!
Title: Re: sequences and series cas help !!
Post by: Hancock on January 24, 2013, 05:23:32 pm: Are S&S even part of Specialist Mathematics? I don't remember learning about them.
Title: Re: sequences and series cas help !!
Post by: Jeggz on January 24, 2013, 05:33:06 pm: Quote from: Hancock on January 24, 2013, 05:23:32 pm
Are S&S even part of Specialist Mathematics? I don't remember learning about them.

yea they included it this year, unfortunately :(
Title: Re: sequences and series cas help !!
Post by: QuantumJG on January 24, 2013, 05:40:20 pm: You guys look at sequences and series now? Awesome!

What is the actual question?
Title: Re: sequences and series cas help !!
Post by: abcdqd on January 24, 2013, 05:46:37 pm: the study design hasn't changed since 2006 and sequences and series isn't in the maths quest book, so it's not going to be on the exams, right?
sequences and series is from GMA, and i think chapter 1 of the essentials book is GMA revision
Title: Re: sequences and series cas help !!
Post by: j23 on January 24, 2013, 11:27:33 pm: Yeah its just in the toolbox. Not sure if it will be in the final exam.

And theres no specific question, i'm just stuck on the whole chapter. Heres an example though!
"A difference equation has rule y(n+1)=2y(n)+6, y(1)=5. Find y(2) and y(3). Use a graphics calculator to find y(10)"

*Note the brackets aren't actually brackets, there the little numbers under the letter! :P
Title: Re: sequences and series cas help !!
Post by: QuantumJG on January 25, 2013, 10:02:39 am: Ok so basically you have a sequence $\{y_n\}$ , where $y_{n+1} = 2y_{n} + 6$ with initial condition $y_1 = 5$ .

The first part is easy:

$y_2 = 2y_1 + 6 = 2\times 5 + 6 = 16$

$y_3 = 2y_2 + 6 = 2\times 16 + 6 = 38$

I have never used a CAS calculator, but this problem can be very easily be done in MATLAB, Mathematica, WolframAlpha?, ... My result is that $y_10$ = 5626.

My code is:

y[1] = 5;
y[n_] := 2*y[n-1] + 6;

This link may be helpful.
Title: Re: sequences and series cas help !!
Post by: j23 on January 25, 2013, 12:45:00 pm: Thanks so much QuantumJG. I've finished all the questions now except one that says
"The fibonacci sequence is given by the difference equation t(n+2)=t(n+1)+t(n) where t1=t2=1. Find the first ten terms of the fibonacci sequence.

And so i type in y[n_] := y[n-1]+y[n-2)
y[1]=1

however whenever i type in my calculator dies and i've done it 5 times! am i typing in something wrong?
Title: Re: sequences and series cas help !!
Post by: QuantumJG on January 25, 2013, 01:37:01 pm: Quote from: j23 on January 25, 2013, 12:45:00 pm
Thanks so much QuantumJG. I've finished all the questions now except one that says
"The fibonacci sequence is given by the difference equation t(n+2)=t(n+1)+t(n) where t1=t2=1. Find the first ten terms of the fibonacci sequence.

And so i type in y[n_] := y[n-1]+y[n-2)
y[1]=1

however whenever i type in my calculator dies and i've done it 5 times! am i typing in something wrong?

Ok, the first part is correct, but you need to include the next condition. So what you need to type is:

y[n_] := y[n-1] + y[n-2]

y[1] = 1

y[2] = 1

The reason why it crashed is because if you tried to find y[3], your calculator would say y[3] = y[2] + y[1], but you didn't define y[2].
Title: Re: sequences and series cas help !!
Post by: BigAl on January 25, 2013, 10:10:08 pm: Series and sequences yay :) :) :) is it the one in further maths or the one that you use epsilon for addition and pi for multiplication?