Sorry everyone, I wasn't able to blog last night because my internet wasn't working. But we had someone come over tonight & fix it so, yay! :)

So far during this unit we've looked at:

**Relations**; "Any set of*Ordered Pairs.*"**Functions**;**Sequences**; " (A specific type of function) A list of numbers that have a particular pattern."

Today, we looked at **Arithmatic Sequences.**

Arethmatic Sequences are a list of numbers where the difference between consecutive terms is the same.

Example: 10 , 12 , 14 , 16 , 18 . . .

Since 10 is the first number in the sequence, it is called *Term One *or T1. 12 is the second number in the sequence, so it is called *Term Two* or T2.

With this sequence, there is a difference of 2 between each term. All Arithmatic Sequences create a straight line. ie: A Linear Equation. ( y = mx + b )

mx = *The difference* *between consecutive terms*

b = T1. ( *Term One*. )

d = *The difference between terms.*

tn = *The Nth Term*.

Here are some more examples that we did together in class...

For the following Arithmatic Sequences, determine the function that represents the list of munbers...

1.) 3 , 6 , 9 , 12 . . .

There is a differnce of 3 between each term, so **d = 3**

This means that the **slope** (or **mx**) is equal to **3/1**

f(x) = 3x [ (x) is the term number. ]

f(1) = 3(1)

f(2) = 3(2) . . . (FUNCTION)

2.) 5 , -3 , -11 , -19 . . .

There is a differnce of -8 between each term, so **d = -8**.

This means that the **slope **( or **mx** ) is equal to **-8/1**

So, starting at 5... take the difference (-8)

**-8 --->5 = 13. (5 - -8 = 13)**

f(x) = -8x+13. (IS NOT A DIRECT FUNCTION)

Now, to find the **Nth** Term...

**tn = t1 + (n-1)d**

t1 = First Term

n = Unknown Number

d = The Difference

Here are some examples...

1.) 8 , 16 , 24 . . . What is the 11th Term? (t11)

There is a difference of 8, so **d = 8**

So.. t11 = 8 + (11-1) 8 ... 8 + (10) 8 = 88 **t11 = 88**

2.) 2.2 , 1.1 , 0 , -1.1 . . . What is the 19th Term? (t19)

There is a difference of 1.1, so **d = 1.1**

So... t19 = 2.2 + (19-1) 1.1 ... 2.2 + (18) 1.1 = 17.6 **t19 = 17.6**

Homework was Excercises 58 (1-8) & 59 (1-11)

The next person to blog is Edward. :P