Math Is Fun Forum / The Nth term and Algebraic Equations (Factorizing/Expanding)

ZainH · 2010-12-04 05:26:33

Hey everyone, this is my first post and I decided I need some help with a coming up math exam. Not something as big as a final, but I still need to get good grades. Unfortunately I forgot my math textbook in my locker and its the weekend, so I was wondering if anyone could maybe give me some questions to work on either from some website they use or a textbook. Questions about the Nth term and expanding and factorizing algebraic equations. Not too complex but not too simple either ;) . Thanks tons.

bobbym · 2010-12-04 05:30:56

Hi ZainH;

What textbook are you using and what type of problems can you do.

Factoring of quadratics? Expanding binomials?

Welcome to the forum!

ZainH · 2010-12-04 05:38:38

Not sure of the exact name but its for IGCSE grade 9.
And expanding questions like.. a(x+y) = ax+ay. But thats wayy to simple, throw in some numbers, squares, cubes, more variables, etc.
No idea what factoring of quadratics are... I wish I had my textbook right now. How about the nth term? Just give a few numbers and Ill try to find the next one.

bobbym · 2010-12-04 05:42:03

Here you go:

5,11,21,35,53,75...

6,14,22,30,38,46...

0,7,26,63,124,215...

ZainH · 2010-12-04 05:44:28

1. 6n-1
2. 8n-2
Give me a little more time on the 3rd one.

ZainH · 2010-12-04 05:45:28

Ahh..
3. N^3 - 1

bobbym · 2010-12-04 05:47:19

Hi ZainH

3) Is correct! As far as correct means in this context.

Sorry but 1 is wrong.

ZainH · 2010-12-04 05:49:36

bobbym wrote:
Hi ZainH

3) Is correct! As far as correct means in this context.

Sorry but 1 is wrong.

Is 3) the only correct one? Or were you just mentioning that because the other two were sort of obvious.
And not sure what you meant by "As far as correct means in this context"

bobbym · 2010-12-04 05:53:48

Hi ZainH;

You and I were posting at the same time, or while I was correcting post #7.

3 is correct but 1 is not.

ZainH · 2010-12-04 06:00:26

I can't seem to find the answer to 1...
Any tricks on solving these?

bobbym · 2010-12-04 06:01:58

There are two main ways for your level. Curve fitting and differences. After that there are many,many more.

ZainH · 2010-12-04 06:04:13

Haven't learnt curve fitting. Differences , I'm assuming is find the difference between the first two terms and that becomes your N then you find what you have to subtract or add to make the equation work?
(I can't solve number 1, whats the answer?)

bobbym · 2010-12-04 06:08:08

Hi ZainH;

You have probably been taught to guess at these. Not quite the best idea.

The answer for 1):

If I would have known that you were being taught like that I would not have given you number 1.

Have you studied simultaneous equations? Differences are pretty easy too.

Want to learn about them? Or want more problems?

ZainH · 2010-12-04 06:12:13

Haven't done simultaneous equations.. and we weren't taught to guess. Our teacher taught us differences. I've got to log off, but if you could post more questions I'd attempt them later and see if I can answer them. If not , I might have to learn about your other methonds.
Thanks for the help

bobbym · 2010-12-04 06:20:05

H ZainH;

Here is something for you to study in the meanwhile:

http://www.mathsisfun.com/algebra/seque … -rule.html

4,7,12,19,28,39...

These two will be a little hard for you, if you have not done your homework!

2,2,4,6,10,16...

2,6,12,20,30,42...

ZainH · 2010-12-05 04:42:33

Hey bobby,
1) N^2 + 3

The link you sent me makes no sense. It brings in two variables to find the answer.
Haven't been taught that so not quite grasping the concept.
I know that for 2) You have to add the two previous numbers to get the next , but can't figure out how to write it as "The nth term"

bobbym · 2010-12-05 08:52:09

Hi ZainH;

1) Is correct.

2) that is good enough that you can get the next one.

What did you get for 3? What was on that page that you did not understand?
Can you be more specific?

ZainH · 2010-12-05 20:34:42

Hey bobby,
I didn't give any thought to 3 but just hold on Ill try to solve it.
(Did you come up with these yourself?)

What I don't understand is , in the method they describe on your link its Xn. Two variables meaning two unknowns.
The method I was described we didn't have x, only n. N would represent the term. For example your question..
1)4,7,12,19,28,39..

For the first term N = 1 , and since the answer is n^2+3 the equation would be .
1^2+3 = 4
Next term N=2... 2^2+3= 7, and so on.

What I don't get is what are they representing by x?

EDIT:
3) N^2 + N

Last edited by ZainH (2010-12-05 20:57:40)

bobbym · 2010-12-05 20:44:08

Is just another way to name variables. The n is called a subscript. You can have lots of variables using subscripts. For instance:

Using just x we can have any number of variables in this way.

Now you can represent a sequence with a rule.

would give:

When you get to linear algebra and difference equations you will be dealing with many variables, hundreds even thousands.
If we just used a to z we could not name them all.

Even with small lists subscripts are useful. Supposing you had 26 numbers and named them a to z.
If I asked you what the fifteenth number in the list is, you would not know offhand that it was o ( the fifteenth letter ).
If you had named them with subscripts you could find the 15th one immediately.
It is

ZainH · 2010-12-05 20:59:53

Hm.. All right, I think I understand.
I edited my last post with the answer to 3). If it didn't show I wrote..
3) N^2+ N

bobbym · 2010-12-05 21:02:31

Hi;

That is correct. Want more?

ZainH · 2010-12-05 21:05:45

Sure.
A question unrelated to the topic, I'm guessing your in university?

bobbym · 2010-12-05 21:11:32

Nope! They forced me out of every school my parents tried to send me to. Some of my teachers, instructors and professors hated me. They said I reasoned like a dog... Woof! Woof! GRrrrr!

Try this one on for size!

0,4,18,48,100

123ronnie321 · 2010-12-05 21:33:55

bobbym · 2010-12-05 21:38:10

Hi 123ronnie321;

I do not have to say that is right. You already know.

ZainH

If that is a little bit too tough yet then here is a slightly easier one.

0,14,78,252,620,1290

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#1 2010-12-04 05:26:33

The Nth term and Algebraic Equations (Factorizing/Expanding)

#2 2010-12-04 05:30:56

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#3 2010-12-04 05:38:38

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#4 2010-12-04 05:42:03

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#5 2010-12-04 05:44:28

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#6 2010-12-04 05:45:28

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#7 2010-12-04 05:47:19

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#8 2010-12-04 05:49:36

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

bobbym wrote:

#9 2010-12-04 05:53:48

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#10 2010-12-04 06:00:26

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#11 2010-12-04 06:01:58

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#12 2010-12-04 06:04:13

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#13 2010-12-04 06:08:08

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#14 2010-12-04 06:12:13

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#15 2010-12-04 06:20:05

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#16 2010-12-05 04:42:33

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#17 2010-12-05 08:52:09

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#18 2010-12-05 20:34:42

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#19 2010-12-05 20:44:08

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#20 2010-12-05 20:59:53

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#21 2010-12-05 21:02:31

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#22 2010-12-05 21:05:45

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#23 2010-12-05 21:11:32

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#24 2010-12-05 21:33:55

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

#25 2010-12-05 21:38:10

Re: The Nth term and Algebraic Equations (Factorizing/Expanding)

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