Is there a mathematician in the house?

If so, are they able to shed light on the subject of Leaving Certificate sequence and series stuff - especially 'Arithmetico Geometric Series'. Something about 'sum of infinity' and other eye crossing figures and heiroglyphics so far as I can see.

A certain leaving certificate student has just been defeated by this topic in her leaving cert mocks and would gretly appreciate advice/help.

Auditor #9 wrote:

https://www.youtube.com/results?search_type=&search_query=tutorial+arithmetic+geometric+sequence+series&aq=f

Thanks for that A9 - very clear tutorial - its about sequences though - the problem is with series - she's unclear about the method for finding the Sn of an arithmetico geometric series - understand the basic premis but the caluclation is the difficult bit. I've been hunting the net too but what I've found so far seems to be too advanced

Howdy Aragon,

There's a nice little slideshow tutorial here titled: "Investigating Sequences and Series." It takes you from simple arithmetic sequences right up to geometric series. A step by step approach with some easy examples. She might be frustrated by having to view the arithmetic stuff.

Tell her not to get frustrated. Some of this stuff requires a lot of elements to be floating around in one's head. The trick to remember is that these elements on their own are simple to understand and deal with. Get her to break this into elements. When you understand and can manipulate each element, complexity is there for the mastering and becomes self-evident. I know that she feels that she understands the premise. But she needs to be able to visualise this in terms of equations and understand how they come about. Calculations become easier when this is achieved.

Aragon, why don't you post one of the questions (possibly an easy one, if such exists) and see if someone will take a bash at it.

Aragon, here is a site I found useful. Though the explanations are general via their examples, the entire structure of sequence and series number is dealt with in totality which might be helpful. Look at the boxes on the lower right hand corner which goes through all the topics on the subject in a logical order. (someone selling something but, hey, it just might do the trick for free.)

www.tutorvista.com/content/math/number-theory/sequences-and-series/sequences-and-series.php

I lurrrved maths in LC but unfortunately I never gave much time to sequence & series, focussing instead on the other questions. Is there any way this certain student could similarly avoid the question?

Post a question or two here Aragon and see how we get on. It's integration if I remember right. It was 18+ years ago though ...

Auditor #9 wrote:

Post a question or two here Aragon and see how we get on. It's integration if I remember right. It was 18+ years ago though ...

Series would not be integration would it? There's a separate integration question.

Series and sequences, arithmetic and geometric ...

Feck - permutations and combinations are coming into my head now ...

No, it's not integration.

For most of these things you learn-off the appropriate formulae (sum(1/n)= blah) and just twist the question until you've reduced it to the formulae you learnt off.

Infinite series of arithmetico geometric series are similar, but there's a trick to the finite series
as demonstrated here:
http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/sequences_and_series/arithmetico_geometric_series___.html
and here:
http://www.mathlinks.ro/Wiki/index.php/Mock_AIME_2_2006-2007/Problem_5

You have to do a bit of unintuitive multiplication and subtraction to the reduce the problem to something simpler.

Friends! Thanks a million for all this advice and help. Here's the sort of question that she's finding difficult:

Find the sum of the first n terms and the sum to infinity of

2 + 5x +8x2 + 11x3 + ...+ (3n-1)xn-1 where |x| <1.

(The exes are 8x to power of 2, 11x to power of 3 - and x to power of n - cant fig out how to make the little floating numbers and letters as they appear in the question. ECU - avoidance of the topic has been her strategy so far but she feels she ought to get her head around the thing really.)

As I said I am unlikely to be able to help with the question but for future reference x to the power of n is generally written x^n where floating numbers are not available. Good luck to her is all I can say.

This is probably a worthwhile ten minutes ...

Khanacademy

It's a specific case of the proof in
http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/sequences_and_series/arithmetico_geometric_series___.html

Plug the following values into his formula and there's your proof:
a=2
d=3
r=x

Cyrus wrote:

It's a specific case of the proof in
http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/sequences_and_series/arithmetico_geometric_series___.html

Plug the following values into his formula and there's your proof:
a=2
d=3
r=x

Cyrus did you see the specific question I posted a bit earlier?

This is from the link that Cyrus gave you. I think he means plug the values into the other values in these boxes. Leave x alone (I think)

The second one is for infinite series ... ?

Or you could just try this weird ITV schools programme - 10 minutes in and I still haven't learned any maths!






https://www.youtube.com/watch?v=GERd72aJ_Z4&feature=related

The confused scholar has asked me to thank everyone very much - she'll be on this thread herself nextweek when the rest of the exams are over. If anyone thinks there is other useful information or advice to give meantime it will be massively appreciated by Aragon Jr.

Hang around with the swots of the class; listen to your teacher; eat fish - good for the brain; bribe the swots of the class to give yourself and your buddies a grind; do as much practice as your brain can take; get fresh air before you study.

You always have amazing sleep and dreams after you study mathematics for the day.

Don't give up - it WILL come to you. And come back here if you need some practice - it might shake the rust out of a few brains around the place.

It's useful to play around with these things on spreadsheets to see how the converge and diverge etc.

If you try to read this in conjunction with the tcd site posted by Cyrus it might help...

Here's what the spreadsheet looks like. Notice each term of the sequeence getting closer to zero.

Also the Sum is nearly 10 after 25 terms.

Thanks a mill EVM - you're a star -