Download an= a1 + (n

November 16, 2015
5.7 Arithmetic Sequences
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
20
,2
5,
30
,3
5 ..
.
November 16, 2015
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...
November 16, 2015
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.
November 16, 2015
Arithmetic Sequences
definition: a sequence created by adding the same number
repeatedly.
Examples
5, 7, 9, 11,...
+2
+2
the number 2 is added to create this sequence.
Here 2 is called the common difference.
7, 3, -1, -5,...
-4
You
try:
+2
-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?
November 16, 2015
Geometric Sequences
definition: a sequence created by multiplying the same number
repeatedly.
Examples:
1, 3, 9, 27,...
x3
x3
the number 3 is multiplied to each term to create
this sequence. Here 3 is called the common ratio.
8, 4, 2, 1,...
÷2
You
try:
x3
÷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?
below.
common
ed to
m, and
.
o find
November 16, 2015
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
November 16, 2015
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
November 16, 2015
Writing an equation for the nth term of
an arithmetic sequence
1. Find a1
2. Find d.
3. Plug in values into the following
equation an= a1 + (n-1)d
Pull
4. Distribute d.
5. Simplify by adding like terms .
6. Now you have an equation to find any
value in the sequence!
- 1)d
November 16, 2015
Write an equation for the nth term of
each arithmetic sequence
Don't
Forget!
18, 25, 32, 39
7n + 11
-14, -5, 4, 13
9n - 23
-110, -85, -60, -35
25n - 135
November 16, 2015
Finding a specific term
Now that we know the formula
an = a1 + (n - 1)d
we can find any of the sequence
1.
a1 = 4
d=6
n = 14
Solution
82
2.
a1 = -4
d = -2
n = 12
Solution
-26
Given th
the valu
your ans
November 16, 2015
November 16, 2015