Download Trig and seq.notebook - Math with Mrs. Brown

Trig and seq.notebook
February 10, 2015
Homework Solutions
Answers to HW #1
1) 24
5) 60
2) 56
6) 5
3)
7) 155
4) 7
Does anyone think they know the answer to this problem without using the calculator?
Check you answer using the calculator...were you correct?
If not can you explain the answer? Trig and seq.notebook
February 10, 2015
Trig and seq.notebook
February 10, 2015
Intermediate Algebra HVCC
Quarter 3
Sequences & Series
Objectives:
• Students can examine sequences & are introduced to
the
notation used to describe them.
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
Which of the following do you think is a sequence?
­10, 10, ­10, 10, ...
1, 2, 3, 4, 5, ....
1, 1, 2, 3, 5, 8, ...
3, 6, 9, 12, ...
Trig and seq.notebook
February 10, 2015
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
us
o
m
t fa
s
o
m
.
The uence..
seq
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
Here are examples of sequences of numbers. Can
you determine the next 3 numbers in the set?
2, 4, 6, 8, ...
1, 3, 9, 27, ...
20, 10, 5, 2.5, ...
Trig and seq.notebook
February 10, 2015
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
There are 2 types of sequences:
Arithmetic
Geometric
An arithmetic sequence
A geometric sequence
goes from one term to the
goes from one term to
next by adding (or
the next by multiplying
subtracting) the same
(or dividing) by the same
value.
Ex.:
value.
2, 5, 8, 11, 14, ...
7, 3, -1, -5, ...
d = 3 5­2=3
8­5=3
d = ­4 3­7=­4
­1­3=­4
Ex.:
1, 2, 4, 8, 16, ...
r = 2 2/1=2
4/2=2
r = 1/3 81, 27, 9, 3, 1, 1/3, ... 27/81=1/3
9/27=1/3
Trig and seq.notebook
February 10, 2015
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
The number added (or subtracted) at each
stage of an arithmetic sequence is called the
because if you
COMMON DIFFERENCE, d,
subtract successive terms, you will always get this
common value.
Ex.: Find the common difference, d, of the following
sequence and find the next term in the sequence:
3, 11, 19, 27, 35
d=8
Next term = 43 (35 + 8)
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
The number multiplied (or divided) at each
stage of a geometric sequence is called the
COMMON RATIO, r, because if you divide
successive terms, you'll always get this common
value.
Ex.: Find the common ratio, r, of the following sequence and
find the next term in the sequence:
‐1/4, 1, ‐4, 16
r = -4
Next term = -64
Trig and seq.notebook
February 10, 2015
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
Determine if each sequence is ARITHMETIC or GEOMETRIC.
Find either the common DIFFERENCE or common RATIO.
Also, find the next term in each sequence.
1. 2, 4, 8, 16, ...
2. 9, 3, 1, 1/3, ...
3. -10, -6, -2, 2, ...
4. -100, -10, -1, ...
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
Determine if each sequence is ARITHMETIC or GEOMETRIC.
Find either the common DIFFERENCE or common RATIO.
Also, find the next term in each sequence.
1. 4, 7, 10, 13, ...
2. 625, 125, 25, 5, ...
3. 1/4, 1/2, 1, 2, ...
4. -11, -14, -17, -20, ...
Trig and seq.notebook
Students can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.
F­IF.A.3
Homework:
Geometric Sequences #1- 6
Arithmetic Sequences #1- 6
February 10, 2015