Q1 - WK2 - L1-2 - Geometric Sequence & Means

GOOD
MORNING! 
Dear God, send Your Holy Spirit
upon us to be our helper and our
guide. Give us the spirit of
wisdom and understanding, the
spirit of right judgement and
courage, the spirit of knowledge
and reverence. Fill us with the
spirit of wonder and awe in your
presence. We pray to the Lord.
Amen.
I say crystal,
you say clear
Math 10:
Quarter 1 – Weeks 3-4
In this lesson, you are expected to:
1) Illustrate a geometric sequence
2) Differentiate a geometric
sequence from an arithmetic
sequence.
3) Determine arithmetic means and
nth term of an arithmetic
sequence
Geometric
Sequence
GEOMETRIC SEQUENCE
1, 2, 4, 8, __, __, __
GEOMETRIC SEQUENCE
•also known as geometric progression
• a sequence where each succeeding
term is obtained by MULTIPLYING
a fixed number (constant)
COMMON RATIO (r)
•fixed number being multiplied to the
sequence
•it may be an integer or fraction, negative
or positive.
•it can be found by DIVIDING any term
by the term that precedes it
EXAMPLES
a) 8, 32, 128, 512

b) 2, -4, 8, -16
c) 10, 20, 40, 80
DO THIS!
Give an example of your

own geometric sequence
with at least five terms.
Geometric
Sequence or
Not?
Determine if the pattern illustrates
1
Geometric Sequence or not:
5, 10, 20, 40, 80,…

GEOMETRIC
SEQUENCE
1
5, 10, 20, 40, 80,…

2
3, 6, 9, 12, 15,…
NOT
2
3, 6, 9, 12, 15,…
3
, , 1, 2…
GEOMETRIC
3
, , 1, 2…
4
1, 3, 9, 27, 81,…
GEOMETRIC
SEQUENCE
4
1, 3, 9, 27, 81,…
5
10, 9, 8, 7, 6,…
NOT
5
10, 9, 8, 7, 6,…
GEOMETRIC
SEQUENCE
3, 8, 13, 18, 23,
OR NOT? …
NOT
r = ____
next 3 terms: Note: No need to give the
____, ____,
value of r and the next 3
____,
terms.
GEOMETRIC
SEQUENCE
-20, 10, -5, ,…
OR NOT?
GEOMETRIC
r = -1/2
next 3 terms: SEQUENCE
-5/4, 5/8, -5/16
Determine if there is a common ratio or
common difference in 6, 12, 14,28,…
solve for d solve for r The sequence is
NEITHER
12 – 6 = 6 12 ÷ 6 = 2 ARITHMETIC NOR
GEOMETRIC
SEQUENCE
14 – 12 = 2 14 ÷ 12 = because it does not
have a common
28 ÷ 14 = 2
28 – 14 = 14 difference nor
common ratio.
Finding the nth
Term in a
Geometric
Sequence
If a1 and r are known, it is
easy to find any term in
geometric sequence using the
rule:
an = a 1 r (n - 1)
GEOMETRIC SEQUENCE
an = a 1 r (n-1)
an = nth term
a1 = first term
r = common ratio
a n = a1 ∙ r (n-1)
Determine the
12 term in
th a12 = 5 ∙ 2(12-1)
the geometric a12 = 5 ∙ 2 (11)

sequence
5, 10, 20,… a12 = 5 ∙ 2 048
a12 = 10 240
a n = a1 ∙ r (n-1)
Determine the
7 term in the
th a7 = 1 ∙ 3 (7-1)
geometric a7 = 1 ∙ 3 (6)
sequence
1, 3, 9,… a7 = 1 ∙ 729
a7 = 729
EXAMPLE 1
Find the specified term of the

geometric sequence:
3, 6, 12,… a9
SOLUTION 1
3, 6, 12,… a9
a9 = 3 ⋅ 2 (9-1)
Number FIRST Number

COMMON
of terms TERM RATIO (r)
of terms
to find (a1) MINUS 1
EXAMPLE 2
Find the geometric term given
the following:
a1 = 2 r = 3
a =?
SOLUTION 2
a1 = 2 r = 3 a6 = ?
a6 = 2 ⋅ 3 (6-1)
Number FIRST Number

COMMON
of terms TERM RATIO (r)
of terms
to find (a1) MINUS 1
Geometric
Means
GEOMETRIC MEANS
the terms between any two
nonconsecutive terms of a
geometric sequence
Find three geometric means between 4 and 64.
What to do?
•Use again the formula:
an = a1 ∙ r (n-1)
to get the value of the common ratio (r)

Find three
geometric
means between
4 and 64.
a n = a1 ∙ r (n-1)
64 = 4 ∙ r (5-1)
Find three
geometric 64 = 4 ∙ r (4)
means between =r 4
4 and 64.
16 = r 4
2=r
4, __,
±8 __
± , __
± , 64
16 32
x x x x
±2 ±2 ±2 ±2
The numbers ±8, ±16, and ± 32 are
the three arithmetic means between
4 and 64.
Insert four geometric means between 9 and 2 187.
What to do?
•Use again the formula:
an = a1 ∙ r (n-1)
to get the value of the common ratio (r)

Insert four
geometric
means between
9 and 2 187.
an = a1 ∙ r(n-1)
a n = a1 ∙ r (n-1)
2187 = 9 ∙ r (6-1)
Insert four
geometric 2187 = 9 ∙ r (5)
means between =r 5
9 and 2 187.
243 = r 5
=r
9, ___
± , ___
± , ±___
243 , ±___
729 , 2187
27 81
x x x x x
±3 ±3 ±3 ±3 ±3
The numbers ±27, ±81, ±243, and
±729 are the four arithmetic means
between 9 and 2187
√
To get the value
of common ratio 𝑛−1 𝒂𝒏
you can also use 𝒂𝟏
the formula: - last term
- first term
n - number of terms in
the sequence
EXAMPLE 1
Insert two geometric

means between 6 and
750.
SOLUTION 1 –To get (r)
a4 = 6⋅r (4-1)
6, ___, ___, 750 750 = 6r 3
an =a ⋅r
1 n-1
125=r 3
±5 = r
√
SOLUTION 1 –To get (r)
𝑛−1 𝒂𝒏
𝑟=
𝒂𝟏
6, ___, ___, 750
𝑟=
4− 1
𝑟 =√ 125
3
√ 750
6
𝒓 =±𝟓
SOLUTION 1.1
6, ±30, ± 150, 750

x ±5 x ±5 x ±5
To be posted in our Google Classroom.
Follow the instructions accordingly.
WK3-4_LT2 Sept. 21
WK3-4_LT3 Sept. 22
(Performance Task)
WK3-4_LT3 (Performance Task)
Create a VLOG regarding your output and may post it in your Facebook
account with hashtags: “#GeometricSequence #Week2PeTa #Math10”
Accomplish the task by creating a PowerPoint or Canva

PRESENTATION and share it in your social media account, using again
the hashtags.
Create a GRAPH showing the geometric sequence of Juan’s total savings
on a bond paper and attach the copy in Google Docs and save it as a
PDF File.
REFLECTIONS FOR WEEK 3-4
https://padlet.com
/jennalynresare/M
ath10
“Life is a
sequence of
moments all
THANK YOU!
GOD BLESS 
Ms. Jennalyn M. Resare

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GOOD

a) 8, 32, 128, 512

Give an example of your

5, 10, 20, 40, 80,…

5, 10, 20, 40, 80,…

the geometric a12 = 5 ∙ 2 (11)

Find the specified term of the

Number FIRST Number

Number FIRST Number

to get the value of the common ratio (r)

to get the value of the common ratio (r)

Insert two geometric

6, _, _, 750 750 = 6r 3

6, ±30, ± 150, 750

Accomplish the task by creating a PowerPoint or Canva

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