September 04, 2014
Get a warm up sheet from the basket.
Pass forward Course Info Signatures.
Precalc Warm Up # 1-4
what does this mean?
1. Find the 20th term in the sequence 7, 11, 15, 19, ...
2. Write a formula that will find the nth term.
3. To check to see if your formula is correct, use
your formula to see if the 4th term was 19.
When you are done, take your student body card and go check out your 2 books. Connie is waiting for us
in the hall.
September 04, 2014
HW Questions ?
#1-3
1. 76(x - 2) + 40 = 3(x + 5)
2.
3.
4.
5.
6.
7. (x-1)(x+5)(x+16)(2x-1)=0
8.
)
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3.
x
4. 3 + 2 = -18(x - 10)
September 04, 2014
September 04, 2014
September 04, 2014
September 04, 2014
From yesterday...
Equation Solving Worksheet.
Name:___________
1. Annie believes she can double the amount of money she has in
her savings account each month. She has $10 at the beginning of
the first month.
$10, $20, $40, $80,....
a. Write an equation that will model the amount of money, y, she
has in the account at the beginning of the xth month. Check to
make sure that when x = 4, y = 80.
b. Without using your grapher, what will be the shape of the
graph?
September 04, 2014
2. Alex believes he can add $10 to his account each month. He
has $1000 at the beginning of the first month.
$1000, $1010, $1020, $1030,...
a. Write an equation that will model the amount of money, y, he
has in the account at the beginning of the xth month. Check to make
sure that when x = 3, y = 1020.
b. Without using your grapher, what will be the shape of the
graph?
September 04, 2014
3. In order to find out how many months it will take for her
account to grow bigger than his, what system would we need to
solve? (you don't have to solve it yet.)
4. Solve the following equations algebraically.
a. 1000 + 10(x-1) = 5000
b. 10 .2
x-1
= 120
5. Why is it more difficult to solve 1000 + 10(x-1) = 10 .2
x-1
?
September 04, 2014
6. Graph the equations from 1a and 2a on the same set of
axis. Be sure to use a good window! What is the answer to
problem 3? Show a sketch of your graph and indicate the
window.
September 04, 2014
The warm up was an example of an
ARITHMETIC SEQUENCE
We are starting a unit which focuses on Arithmetic
sequences and series and Geometric sequences and
series.
There are many others.
Quadratic, Fibonocci, ect....
Quadratic: 1,4,9,16,25,...
formula: an=n2
Fibonocci: 1,1,2,3,5,8,13,...
formula: an=an-1+an-2 , a1=a2=1
I wrote the quadratic formula EXPLICITLY, and I wrote the
Fibonocci formula RECURSIVELY.
September 04, 2014
Arithmetic sequences (AP) have a
CONSTANT DIFFERENCE, d.
The nth term is given by the following formula.
an= a1 + d(n-1)
1. Find the 100th term in -4, -1, 2, 5, ...
2. If the first term in an AP is 6 and the 20th term is
-70, find the 10th term.
September 04, 2014
3. Find a formula for the nth term in an arithmetic
sequence if the first term is 8 and the 4th term is
-10. Hence, find the 100th term.
September 04, 2014
Groups:
4. If the 5th term is 20 and the 14th term is 74 in
an AP, find the first term and constant difference.
HENCE find the 100th term.
September 04, 2014
4. If the 5th term is 20 and the 14th term is 74 in
an AP, find the first term and constant difference.
One Way:
5
_ _ _ _ 20
_ _ _ _ _ _ _ _ _ 74
_
HENCE find the 100th term.
pros and cons?
14
September 04, 2014
4. If the 5th term is 20 and the 14th term is 74 in
an AP, find the first term and constant difference.
Another way: Think of these as points, and since arithmetic is
linear,
there will
be a
constant
slope.
HENCE find the 100th term.
pros, cons?
September 04, 2014
4. If the 5th term is 20 and the 14th term is 74 in
an AP, find the first term and constant difference.
A third way is to solve a System:
a5 = a1 + d(5-1) = 20
a14 = a1 + d(14-1) = 74
HENCE find the 100th term.
pros, cons?
September 04, 2014
5. Find the rule that gives the nth term for
y-3, y, y+3, y+6,......
Then find the tenth term
September 04, 2014
In groups,
6. If 2x - 1, x + 9, 3x + 4
terms in an AP, find x.
Then find the tenth term
are consecutive
September 04, 2014
#1-4 p. 244 1-14
Remember, the homework quiz is coming up on Tuesday.