GEOMETRIC SEQUENCES
Recall that arithmetic sequences
have a common difference (d).
Example: 4, 7, 10, 13, …
Common Difference (d) = 3
GEOMETRIC SEQUENCES
Geometric sequences have a
common ratio (r).
Example: 3, 6, 12, 24,…
Common Ratio (r) = 2
Each term can be found by multiplying the
preceding term by the common ratio (r).
FLASH CARDS
Geometric or Arithmetic?
Next Term?
51
47, 48, 49, 50, _____
ARITHMETIC
FLASH CARDS
Geometric or Arithmetic?
Next Term?
9
-3, 0, 3, 6, _____
ARITHMETIC
FLASH CARDS
Geometric or Arithmetic?
Next Term?
80
5, 10, 20, 40, _____
GEOMETRIC
FLASH CARDS
Geometric or Arithmetic?
Next Term?
-32
-2, 4, -8, 16, _____
GEOMETRIC
FLASH CARDS
Geometric or Arithmetic?
Next Term?
7.5
1.5, 3, 4.5, 6, _____
ARITHMETIC
FLASH CARDS
Geometric or Arithmetic?
Next Term?
1/
2,
1/ , 1/ , 1/ ,
4
8
16
1/
32
_____
GEOMETRIC
GEOMETRIC SEQUENCES
To find the common ratio (r) of a
geometric sequence, divide any
term by the preceding term.
Find the common ratio for
3, 6, 12, 24, …
r= 6÷3 =2
r = 12 ÷ 6 = 2
FLASH CARDS
What is the common ratio?
Next Term?
-80
-5, 10, -20, 40, _____
r = -2
FLASH CARDS
What is the common ratio?
Next Term?
3.75
60, 30, 15, 7.5, _____
r = 0.5
FLASH CARDS
What is the common ratio?
Next Term?
81
16, 24, 36, 54, _____
r = 1.5
FLASH CARDS
What is the common ratio?
Next Term?
768
3, 12, 48, 192, _____
r=4
GEOMETRIC SEQUENCES
To find the nth term of a
geometric sequence
an = a1
n-1
(r )
Find the seventh term: 3, 6, 12, 24, …
a7 =
7-1
3(2 )
= 3(64) = 192
GEOMETRIC SEQUENCES
To find the nth term of a
geometric sequence
an = a1
n-1
(r )
Find the tenth term: 4, 6, 9, 13.5, …
a10 =
10-1
4(1.5 )
= 4(38.443)
= 153.773
GEOMETRIC SEQUENCES
Missing terms between two
nonconsecutive terms in a geometric
sequence are called GEOMETRIC MEANS
To find one geometric mean
between a & b
ab
GEOMETRIC SEQUENCES
Find the geometric mean of 4 and 9.
4, ____, 9
4(9)  36
 6
GEOMETRIC SEQUENCES
Find the geometric mean of 2 and 32.
2, ____, 32
2( 32)  64
 8