Transcript Agenda 1/8 & 1/9

Agenda 1/8 & 1/9
•
•
•
•
•
•
Warm up
What’s My Pattern?
Arithmetic Sequences
Function Formula
Explicit / Closed Form
Homework
Warm UP
A square table seats 4 people. Two square
tables pushed together seat 6 people.
Three tables pushed together seat 8
people. How many tables are needed to
seat 22 people?
What’s My Pattern?
Math 8 Unit 4 Task
Work with your partner to complete
questions number 1.
What’s My Pattern?
How did you do???
a) 6,7,8
b) 17, 19, 21 c) -5, -8, -11
d) 22, 29, 37 e) 4, -4, 5
f) 36, 49, 64
g) 11, 12.5, 14
h) -4, -8.3, -12.6
i) 95, 191, 383
j) 13, 21, 34
Now do question 2.
What’s My Pattern?
A sequence is an ordered list of numbers.
Each number in the sequence is called a
term.
The first term,7, of the second sequence,
(sequence b), is labeled as b1. You read it
as “b sub one”. The second term,9, is
labeled b2, the third, 11, is b3, and so on.
Now do question 3.
What’s My Pattern?
Here is one to try on your own:
k) 2, 4, 6, 8, 10, 12, 14, 16, ___, ___, ___
2 is the 1st term (k1), 10 is the 5th term (k5),
and 16 is the ____ term.
What is the 10th term (k10)? __________
Arithmetic Sequences
An arithmetic sequence is a sequence in which
each term is equal to the previous term plus a
constant. The constant is called the common
or constant difference. We use the letter d to
represent the constant difference.
We use the letter n to tell us which term number
we want.
There are several ways to write a “formula” for
these sequences.
Arithmetic Sequences
Why would we want to write a formula?
How would you find the 6th term of the
following sequence? 8,15,22,29,…
What about the 10th term?
What about the 20th term?
How about the 50th term, or the 100th term?
There comes a time when a formula would
be helpful!!
Function Formula
First formula…..Function Formula. (BTW,
these are only for ARITHMETIC SEQ’s!!)
1) Formula: y = dn + _?_ (I call this the adjuster)
2) Determine what is happening to your
pattern. Find the constant difference,d.
3) Pick a term in the sequence. You will get
2 pieces of information from this term: y
is the actual value and n is the term
number.
Function Formula
4) Sub d, n and y into y=dn+ ___ and find
out what number needs to fill in the
blank. (d is ALWAYS in front of n!)
5) You now have what you need to write
your formula: d and the number that
goes in the blank (adjuster)
Try the following sequences:
a) 8, 15, 22, 29, ….
Function Formula
b) 100, 93, 86, 79, …
c) 2, 5, 8, 11, ….
d) 11, 7, 3, -1, …
Function Formula
Once you have the formula you can find any
term, the 15th, the 35th, the 100th, etc…
Let’s use the function formula from
sequence a: y =__________
a) Find the 15th term
Function Formula
b) Find the 30th term.
c) Find the 50th term.
Explicit / Closed Form
2nd Formula: Explicit / Closed Form and the
Recursive Definition
The Explicit / Closed form is written almost
the same way. Everything is the same,
EXCEPT, instead of y we use tn.
1) Formula: tn = dn + _?_ (I call this the adjuster)
Explicit / Closed Form
2) Determine what is happening to your pattern.
Find the constant difference, d.
3) Pick a term in the sequence. You will get 2
pieces of information from this term: tn is the
actual value and n is the term number.
4) Sub d, n and tn into tn =dn+ ___ and find out
what number needs to fill in the blank. (d is
ALWAYS in front of n!)
5) You now have what you need to write your
formula: d and the number that goes in the
blank (adjuster)
Explicit / Closed Form
Try the following sequences:
a) 8, 15, 22, 29, ….
b) 100, 93, 86, 79, …
c) 2, 5, 8, 11, ….
d) 11, 7, 3, -1, …
Explicit / Closed Form
Once you have the formula you can find any
term, the 15th, the 35th, the 100th, etc…
Let’s use the function formula from
sequence c: tn =__________
a) Find the 15th term
Explicit / Closed Form
b) Find the 30th term.
c) Find the 50th term.
Arithmetic Sequences
We will work on practicing these more
next class.
Homework
• Worktext p.421 and 422, all