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Transcript
Arithmetic and Geometric
Sequences
Sequences
Numbers can be written in a pattern, such as the
following: 3,9,27, 81….
Do you know the pattern?
Everything is being multiplied by 3.
A number pattern can be referred to as a
sequence.
There are two types of sequences: an arithmetic
sequence and a geometric sequence.
Number Patterns
The numbers in a sequence are called
terms of the sequence.
An arithmetic sequence is formed by
adding a fixed number to each previous
term. This number is called the common
difference.
What is an arithmetic
sequence?
A sequence in which
each term is found by
ADDING the same
number to the previous
term.
+4
4,
+4
+4
+4
8, 12 , 16, 20…………..
What is the common
difference?
The difference between
each number. This
determines what is added to
each previous number to
obtain the next number.
4, 8, 12, 16, 20…………..
4 is the common difference
A.
B.
C.
Arithmetic Sequences
Find the common difference of each
arithmetic sequence.
a. -7, -3, 1, 5
b. 17, 13, 9, 5
c. Common difference is 4.
d. Common difference is -4.
Special Note: If there is no common difference,
the sequence is not arithmetic.
Geometric Sequences
You form a geometric sequence by
multiplying a term in the
sequence by a fixed number to
find the next term. The fixed
number is the
common ratio.
What is a geometric
sequence?
A sequence in which
each term can be found
by multiplying the
previous term by the
same number.
x3
3,
x3
x3
x3
9, 27 , 81, 243…………..
What is the common ratio?
The number used to multiply
by each previous number to
obtain the next number.
2, 8, 32, 128, 512…………..
4 is the common ratio
What is the next term in this
sequence?
x4
x4
x4
x4
5, 20, 80, 320 , _____
1,280
What is the next term in this
sequence?
X-2
X-2
X-2
X-2
-3, 6, -12, 24 , _____
-48
Is this an arithmetic or
geometric sequence?
10, 15, 20, 25, 30……
Arithmetic Sequence
+5
5 is the common difference
Is this an arithmetic or
geometric sequence?
2, 12, 72, 432, 2,592……
Geometric Sequence
x6
6 is the common ratio
A.
B.
C.
D.
Sequence 1
Sequence 2
Sequence 3
Sequence 4