Download 4.6 Arithmetic Sequences 20, 25, 30, 35

4.6 Arithmetic Sequences
How can you use an arithmetic sequence to describe a pattern?
20
,2
5,
30
,3
5 ..
.
Figure #
# of circles
30
25
20
15
10
5
Patterns
definition: a pattern is any group of
objects or numbers that follow a rule.
1, 4, 16, 64...
3, 6, 9, 12...
2, 6, 4, 8, 6...
Sequences
2, 4, 6...
definition: an ordered set of numbers that follows a rule.
1, 2, 3, ....
20, 25, 30, 35...
100, 10, 1, .1,...
3, 9, 27, 81...
1, 1, 2, 3, 5, 8...
There are two types of sequences we'll look at this year:
arithmetic and geometric.
Arithmetic Sequences
definition: a sequence created by adding the same number
repeatedly.
Examples
5, 7, 9, 11,...
+2
+2
7, 3, -1, -5,...
-4
You
try:
+2
the number 2 is added to create this sequence.
Here 2 is called the common difference.
-4
-4
In this example we are subtracting 4 or adding a -4,
so we say the common difference is -4
-3, 2, 7, 12,... What is the common difference?
Geometric Sequences
definition: a sequence created by multiplying the same number
repeatedly.
Examples:
1, 3, 9, 27,...
x3
x3
8, 4, 2, 1,...
÷2
You
try:
x3
the number 3 is multiplied to each term to create
this sequence. Here 3 is called the common ratio.
÷2
÷2
In this example we are dividing by 2 or multiplying
by 1/2, so we say the common ratio is 1/2
-3, -6, -12,... What is the common ratio?
ers below.
nd a common
added to
d term, and
...etc.
ue to find
ms.
Common Difference
Hint: Erase to Reveal Solution
common difference the common difference between two
consecutive elements of a sequence
1. 7, 11, 15, 19, 23, 27, 31
2. -4, -6, -8, -10, -12, -14, -16
3. 15, 7, -1, -9, -17, -25, -33
Given First Term and Common Difference
Hint: Move to Reveal Solution
a1 = the first term of an arithmetic sequence
d = the common difference (value add to each term to find the
next term)
Find the first five terms of each sequence. Check your solution
by moving the question to the solution box.
Question
1. a1= 6 d = 9
6, 15, 24, 33, 42
2. a1 = -60 d = 4
-60, -56, -52, -48, -44
Solution
Write the next three terms of the arithmetic sequence.
1. −12, 0, 12, 24, . . .
2. 0.2, 0.6, 1, 1.4, . . .
3.
Does the graph represent an arithmetic
sequence? Explain.
an - value of the nth number in the sequence
a1 - first number in sequence
n - step number
d - common difference
an= a1 + (n - 1)d
Write an equation for the nth term of the arithmetic sequence 14, 11, 8,
5, . . .. Then find a50.
an= a1 + (n - 1)d
Don't
Forget!
(n - 1)d
Write an equation for the nth term of the arithmetic sequence.
Then find a25.
a. 4, 5, 6, 7, . . .
b. 8, 16, 24, 32, . . .
c. 1, 0, −1, −2, . . .
Don't
Forget!
Online bidding for a purse
Bid Number
1
increases by $5 for each bid
Bid Amount
$60 $65 $70 $75
2
3
after the $60 initial bid.
a. Write a function that represents the arithmetic sequence.
b. Graph the function.
c. The winning bid is $105. How many bids were there?
4
A carnival charges $2 for each game after you pay a $5 entry fee.
a. Write a function that represents the arithmetic sequence.
b. Graph the function.
c. How many games can you play when you take $29 to the carnival?
Games
1
2
3
4
Total Cost
$7 $9 $11 $13
Pg 214: 1-15odd, 19, 24-36e, 46-48,
62-65
3-2-1: Hand out a reflection sheet as described in the Formative
Assessment Tips.
Use the table to find the slope.
1. x 2
3
4
5
2. x 14 28 42 56 70
y 17 20 23 26 29
y 4
11 18 25
3. x 5
21 37 53
4. x 0
4
8
27 43 49
y 4
8
12 16 20
y 11
12 16
Tell which number you would add to or subtract from each side of
the inequality to solve.
1. k − 12 > −4
2. 0 ≤ b + 8
3. x + 5 > −6
4. 7 ≤ m + 2
5. r − 2 > 6
6. 8 + w > 8
Work with a partner. Use the figures to complete the table. Plot
the points given by your completed table. Describe the pattern of
the y-values.
Graph the arithmetic sequence 4, 8, 12, 16, . . .. What do you notice?
Graph the arithmetic sequence. What do you notice?
4. 3, 6, 9, 12, . . .
5. 4, 2, 0, −2, . . .
6. 1, 0.8, 0.6, 0.4, . . .
7. Does the graph shown represent an arithmetic sequence? Explain.