PREPARED BY:
MARICEL P. ABLAZA
GRADE 10 - TEACHER
Barbarian King of clan
Algorithm, Please! Help us!
There is a dengue outbreak in
Sipnayan Clan. And during the initial
phase the number of dengue
mosquitoes can grow geometrically.
Six days ago, there were 12, 24, 48… ,
on the first three days of the outbreak.
Thank You!
What’s wrong Archer Queen?
That’s already alarming! We will join
force to help your clan to control the
dengue outbreak.
Your welcome!
Before we proceed… Let me teach you how to find the number of mosquitoes after
six days through geometric sequence.
A geometric sequence is a sequence where each term after the
first is obtained by multiplying the preceding term by nonzero constant
called ratio.
The common ratio, r , can be determined by dividing any term
in the sequence by the term precedes it.
Example:
Find the ratio of the following.
=2
1. 5, 10, 20…
r=
2. 256, 128, 64, 32…
r=
Given the first term and common ratio, r , of a geometric sequence, the
term of a geometric sequence is .
Now, consider the number of dengue mosquitoes on the first three days of the
outbreak 12, 24, 48
Therefore, we need to destroy 384 dengue mosquitoes.
ADDITIONAL
INFORMATION
To solve for the value of
Find
, if the common ratio is 3
Solution: Given r = 3 n = 5
405 =
405 =
To solve for the value of RATIO
If
Given:
substitute
192 = (-3)
192 = -3
substitute
divide both side by -3
evaluate the exponent
divide both side by 81
-64 =
5 =
extract the root
-4 = r
Deploy the following troops according to the number of mosquitoes they can eliminate. You will
successfully deploy the troops once you solve the value of nth term.
1 a1 = 5
r = 20 a 2
2. 1200, 600, 300… a
3. 2, 4, 8… a
6
5.
4. 1620, 540, 180… a
r=5
5
20
125
75
5
64
100
This is the key to prevent dengue outbreak. Decode the mystery word by solving the following
geometric sequence. Write the letter that corresponds to your answer on the blanks to complete the word.
__ __ E __ __ __ I __ E __ __
4
1.
2.
3.
4.
5.
2
3
5
2
5
1
1
Given r = 2, n=7 a n = 192 , find a
Find r in the geometric sequence if the first term is 1/3 and the eighth term is 128/3
Find the tenth term of the geometric sequence 2, 4, 8 …
Find the ninth term of the geometric sequence x, 2x, 4x…
Identify the common ratio of 2, -8, 32, -128…
Archer Queen felt very grateful to Algorithm Clan she sent a chain text
message to 3 friends at 7:00 A.M. saying, “ Thank you and God bless”, and they
each then passed the text message to 3 new people within the hour, and so on. The
number of recipients of the text message every hour forms a geometric sequence.
Time
7 AM
8 AM
No. of Text Recipients
1
3
9 AM
10 AM
11 AM
12 PM
How many people have received the text message by 10 AM? By 1 PM?
1 PM
SPECIAL THANKS TO:
Jerry D. Cruz, et al , Mathematics Learner’s
Module for Grade 10, page 27, publication,
REX Book Store, Inc.
Gladys C. Nivera , Intermediate Algebra page
288, publication, Salesiana Publishers, Inc.
ACTIVITY CARD
1. 64
2. 75
3. 100
4. 20
5. 125
ASSESSMENT CARD
1. 3
2. 2
3. 1024
4. 8x
5. -4
CLEANLINESS
ENRICHMENT CARD
10 A M – 27 RECIPIENTS
1 P M – 729 RECIPIENTS
FINAL
OUTPUT