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Arithmetic Sequences

Sorry I haven't written in 5 days. I've recently had an addiction to Squidoo and Helium. Hey. I like money after all.

However I'm working out a new writing schedule so that I can incorporate my new addictions without forgetting about my blog ♥

Here's a post I was working on:

Old class notes: MATH

Arithmetic sequences:

Recursive: Figuring out a sequence step by step
Explicit: Figuring out a sequence from a general formula.
Arithmentic: Common diference between the terms.
a) recursive: an = an-1 +d
b) explicit: an = a1 + d(n-1)

example:
-6, -2, 2, ....
a1,a2,a3,....

Common difference (d): +4.

Example:
Finding the 10th term recursively. (the slow inconvenient way)
Recursive: an = an-1 + 4.
That means if (for example) you want to find the 4th term (a4) you'd have a4 = a3 +4. That means you need to know a3 to find a4 (and you need to know a4 to find a5, etc..)
In short it means: start at the beginning and add.
a1, a2, a3, a4, a5, a6, a7, a8, a9, a10
-6, -2, 2 , 6 , 10, 14, 18, 22, 23, 30

Finding the 10th term explicitly. (the fast way)
explicit: an = a1 + 4(n-1).
a1 is the first term , which in this case is -6.
explicit: an = -6 + 4(n-1). So if you want to find the 10th term (a10), you'd have a10 = -6 +4(10-1).
which comes out to
a10 = -6 + 4(9)
a10 = -6 + 36
a10 = 30.

What if you're not given the first term? If you're given any term (and told what the term number is) you can still use this method. However you'll have to adjust. For example, if you were given the 4th term and needed to find the 10th term, in truth you make the 4th term become term 1, and the 10th term becomes term 6 (10-4).

What if you're not given the term numbers? Then you'll have to use Recursive. Sorry.

TI-83 Calculator Trick

I once wrote a program for my Ti-83 that would use the Quadratic formula for me:
A=-B +-V(b2-4AC)
all over 2A

All you have to do is:

1. Turn your calculator on
2. Press the Prgm button
3. Go right twice to New
4. Press Enter (Create new)
5. Give it a name (ideally one your teachers won't recognize. I called it "Lupu")
6. Copy the code on the right.

What's with the colored words?
These are not words you write. These are words written within the calculator's library.
While you are writing your program, press Prgm again to see the library.

PS.The colons appear by pressing Enter.

Disp is found in the I/O section, 3d word.
-Go to Prgm.
-Go right once
-Go down twice (or press 3)

Pause is found in the CTL section of the library, 8th word.
-Go to Prgm
-Go down 7times (or press 8)

Prompt is found in the I/O section, 2d word
-Go to Prgm
-Go right once
-Go down once (or press 2)

What does this program do?
It will ask you for three numbers. These are a, b, and c.
In the equation:
5x^2 +3x + 4 =0
a=5
b=3
c=4
The equation MUST be in this format for you to enter the numbers in the right order.

The program will then step-by-step solve for x.
This means it's easy to copy the steps down.

For example:
if I enter:
1
3
2

It will say
"
-3
+-V()
1
/
2
"

so x= -3 +-V(1)
all over 2.

The program will pause at this point so you can copy this down.
It will then proceed to solve for x if you press Enter. If it's an imaginary answer it will crash and you just press Quit.
After all, you already have the hard part done.
If it's not an imaginary answer, it will tell you x.
Using this example, the program would continue and say
"Roots
-1
-2
"
So the roots of the equation would be x=-1 and x=-2

So what's this program good for?
Well it allows you to know the equation in Quadratic formula form without you having to remember or do any math, thus making you look as if you know your stuff. I'm good at math so I only used this because I was lazy, not because I didn't know it.

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