Find the missing terms.
64 128
1. 2, 4, 8, 16, 32, ___,
___
multiplied by 2
Find the missing terms.
1
1
3
2. 81, 27, 9, ___, ___,
3
𝟏
multiplied by
𝟑
Find the missing terms.
40 -80
3. −5, 10, −20, ___,
___
multiplied by –2
Find the missing terms.
-8 ___
4
4. 64, −32, 16, ___,
𝟏
multiplied by −
𝟐
Find the missing terms.
24 -48
5. −3, 6, −12, ___,
___
multiplied by –2
Find the missing terms.
𝟗
−
−
9
6. −72, −36, −18, ___, ___𝟐
𝟏
multiplied by
𝟐
GEOMETRIC
SEQUENCE
GEOMETRIC SEQUENCE
A sequence where each term after
the first is obtained by multiplying
the preceding term by the same
constant called common ratio.
GEOMETRIC SEQUENCE
Tell if the ff. is a GEOMETRIC Seq. or Not. If
GS give the common ratio.
1
1. , 1, 4, 16, 64, … r=4
4
NOT
2. 2, 4, 6, 8, …
Geometric seq.
GEOMETRIC SEQUENCE
Tell if the ff. is a GEOMETRIC Seq. or Not. If GS
give the common ratio.
NOT
3. −3, −6, −9, −12, …
𝟏
4. 120, 60, 30, 15, … r=𝟐
Geometric Seq.
Tell if the ff. is a GEOMETRIC Seq. or Not. If GS
give the common ratio.
5. 3, 12, 48, 192, 768, …
r=4
Geometric Seq.
2
4
6
8
6. 5𝑥 , 5𝑥 , 5𝑥 , 5𝑥 , …
Geometric Seq.
r=𝒙
𝟐
GEOMETRIC SEQUENCE
𝒏−𝟏
𝒂𝒏 = 𝒂𝟏 𝒓
th
n
term
Number
st
1
Common
of terms
term
ratio
GEOMETRIC SEQUENCE
th
1. Find the 8 term of the geometric sequence
4, 8, 16, 32, 64,….
𝒏−𝟏
𝒂𝒏 = 𝒂 𝟏 𝒓
a8 =
8–1
4(2)
a8 = 4(128)
a8 =
7
4(2)
a8 = 512
GEOMETRIC SEQUENCE
th
2. What is the 7 term of the geometric
sequence
2 2
10, 2, , , … ?
5 25
𝒂𝒏 = 𝒂𝟏
𝒏−𝟏
𝒓
𝟕−𝟏
𝟏
a7 = 10
𝟓
𝟏 𝟔
a7 = 10
𝟓
a7 =10
𝟏
𝟏𝟓𝟔𝟐𝟓
𝟏𝟎
a7 =
𝟏𝟓𝟔𝟐𝟓
𝟐
a7 = 𝟑𝟏𝟐𝟓
3. Which term of GS -4, 12, -36, 108, … is
𝒏−𝟏
-2916?
𝒂𝒏 = 𝒂 𝟏 𝒓
n
1
(-3)
-2916 = -4
-4
-4
n
1
729 = (-3)
?
n
1
(-3) = (-3)
GEOMETRIC SEQUENCE
3. Which term of GS -4, 12, -36, 108, … is -2916?
n
1
(-3)
729 =
?
n
1
(-3) = (-3)
6
n
1
(-3) = (-3)
th
7
6=n–1
term
7=n
GEOMETRIC SEQUENCE
1
1
th
4. If common ratio is and its 10 term is ,
2
64
then find 𝑎1 .
𝒏−𝟏
𝒂𝒏 = 𝒂 𝟏 𝒓
𝟏
𝟏
= 𝒂𝟏
𝟔𝟒
𝟐
𝟏𝟎−𝟏
GEOMETRIC SEQUENCE
𝟏
𝟏
= 𝒂𝟏
𝟔𝟒
𝟐
𝟏
𝟏
= 𝒂𝟏
𝟔𝟒
𝟐
𝟏𝟎−𝟏
𝟓𝟏𝟐
= 𝒂𝟏
𝟔𝟒
𝟗
𝟏
𝟏
= 𝒂𝟏
𝟔𝟒
𝟓𝟏𝟐
𝟖 = 𝒂𝟏
𝒂𝟏 = 𝟖
GEOMETRIC SEQUENCE
th
th
5. What is the 10 term of GS with 32 as the 4 term
and 2 as common ratio?
𝒂𝒏 = 𝒂𝟏 𝒓
𝒏−𝟏
𝒂𝟏𝟎 = 𝒂𝟒 𝒓
?−𝟏
𝒂𝟏𝟎 = 𝟑𝟐 𝟐
𝟕−𝟏
𝒂𝟏𝟎 = 𝟑𝟐 𝟐
𝟔
𝒂𝟏𝟎 = 𝟑𝟐(𝟔𝟒)
𝒂𝟏𝟎 = 𝟐𝟎𝟒𝟖
GEOMETRIC MEANS
The terms between any two given
terms of a geometric sequence
81, 27
27, 9
2, 4, 8, 16
16, 32
GEOMETRIC MEANS
Insert 3 geometric means between 3 and
48
3, _, _, _, 48
an =
n-1
a1r
a1 = 3
48 =
5-1
3r
a5 = 48
48 = 3r4
3
3
r=?
n=5
16 =
4
4
r
4
16 = r4
 2 = r
GEOMETRIC MEANS
3, _, _, _, 48
6, 12, 24
3, _, _, _, 48
-6, 12, -24
GEOMETRIC MEANS
There are 5 Geometric Means between 4 and 2916.
Find the 3rd geometric mean.
a4=?
r=?
a1=4
4, _, _, _, _, _, 2916
a7=2916
2916=4r6
4
4
n=7
an=a1
n-1
r
7-1
2916=4r
729= r6
6
6
729 = r6
 3=r
GEOMETRIC MEANS
3
3
3
12 __,
36 108
4, __,
__, __, __, 2916
rd
3
geometric mean =a4 =108