Tuesday, January 16, 2007
posted by DestiniLyn at 7:01 PM
Monday, January 15, 2007.

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." Example: (0,1) (2,3) (2,7) (-3,9) ...
  • Functions ; " (A type of Relation) Each x value can only have one corresponding y value."
  • 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

 



3 Comments:


At August 24, 2012 6:30 AM, Anonymous Free Math Homework Help

As a maths teacher I am working on these topics and want a simple and easy process to describe arithmetic sequence.