ACTIVITY SHEET IN MATHEMATICS 10
NAME: ______________________________________ SCORE:______________
GRADE LEVEL:___________________
WEEK: 1
Task 1: Tell whether the given numbers form a sequence or not.
1. 6,
13
15
17
2
2
2
, 7,
, 8,
,…..
2. 12, 13, 17, 19, 22, ….
3. 63, 127, 255, 511, 1023,…..
4. 28, 31, 34, 37, 40, ….
1 3
1
4 7
1
2
3
5
2
2
2
5. , , 3, 5, , ……
6. − , 1, − , 2, − , 3, ……..
7. -3, -1, 0, 4, 5, …..
1
1 2 1
8. -2, − , 0, , , ,……..
2
4 3 8
9. 1, , ,
,
4 5 2
5
, ……
5 5 17 13
5
7
9
10. 2, , 3, , 4, , ….
2
2
2
Task 2: Describe the pattern formed. Find the next three terms.
1. 1, 4, 7, 10, ……..
2. 4, -8, 16, -32, …….
1 1 1
3. , , , ……..
2 4 8
4. 0, 3, 7, 12, 18 ……
5. 1, 3, 9 ……….
Task 3: In a Physics experiment, a ball is dropped at the height of 24 feet. For
each time it bounces, the ball reaches half its previous height. Below is the table
showing the height of the ball bounces until it comes to rest. What will be the
height of the ball if it bounces on the 4th ,5th, 6th and 7th time?
No. of
1
2
3
4
5
6
7
Bounces
Height
12
6
3
(ft)
_____________________
Math Teacher
Parent’s Name/Signature
ACTIVITY SHEET IN MATHEMATICS 10
NAME: ______________________________________ SCORE:______________
GRADE LEVEL:___________________
WEEK: 2
Task 1: Tell whether the following sequence form an arithmetic sequence .
1. 12, 17, 22, 27, 32, ……
2. 15, 11, 7, 3, -1, …..
3. 1, 1, 2, 3, 5, 8
4. 4, 16, 64, ……
5. 100, 50. 25, 25/2…
6. -3, -5, -7, -9, ….
7. 8, -4, 2, -1, …
8. 5, 5.5, 6, 6.5 ……
9. 20, 17, 14, 10, ….
10. 11, 16, 21, 27, …….
Task 2A: Find the next 5 terms of each of the given arithmetic sequences.
1.
2.
3.
4.
5.
3,6,9,12……..
5,9, 13,…….
21, 15, 9 ….
2, -3, -8, ….
11, 8, 5……
Task 2B: Solve the following arithmetic sequences and name the first 4 terms.
1. 𝑎1 = 4, 𝑑 = 3
2. 𝑎1 = 7, 𝑑 = 5
3. 𝑎1 = −8, 𝑑 = 3
1
1
2
2
4. 𝑎1 = , 𝑑 =
5. 𝑎1 = 6, 𝑑 = −2
Task 3: Solve each problem. (Show your solution on the space provided)
1. What is the 12th term of the arithmetic sequence 5, 8, 11, 14,…?
2. What is the common difference of an arithmetic sequence if the first term
is 12 and the 10th term is 39?
3. The given sequence -37, -33, -29, …form an arithmetic sequence, what will
be the 10th term of the sequence?
4. Michael deposited Php20,000 on an investment that will give Php1,750 for
every year that his money stays in the account. How much money will he
have in his account by the end of year 10?
5. Sarah works in a law firm with a beginning salary of Php450,000 per year. If
her salary will be increased yearly by Php2,000, what would be her salary
on the 10th year of working?
_____________________
Math Teacher
Parent’s Name/Signature
ACTIVITY SHEET IN MATHEMATICS 10
NAME: ______________________________________ SCORE:______________
GRADE LEVEL:___________________
WEEK: 3-4
Drill:
1. What is the 10th term of the sequence 2, 5, 8….?
2. What is the common difference of the sequence in #1?
3. How can we tell if the given the sequence is an arithmetic sequence? Explain
your answer.
_____________________________________
The teacher will give a preliminary problem and the students will be asked to see the
difference from the previous lesson discussed to them. This will lead the students to the
next topic.
GEAR UP: Find the next 4 terms.
1. 3, 6, 12, 24, ……….
2. 1, 3, 9, 27 ………..
3. ½, ¼,1/8, …….
4. 80,40, 20……..
5. 400,200,100….
Questions:
1. Hoe did you arrive with your answer?
2. What operations were used?
3. What makes the sequence different from the previous lesson discussed?
KEY IDEA
A geometric sequence or progression is a set of terms in which each term after the first
is obtained by multiplying the preceding term by the same fixed number called the
common ratio which is commonly represented by r.
If the common ratio is greater than 1, the sequence grows at an increasing rate. Thus,
the common ratio is known as the growth factor.
If the common ratio is less than 1, the sequence shrinks at a decreasing rate. Thus, this
common ratio is known as the decay factor.
Let Us Practice!
In the given example: 2, 6, 18, 54, 162, . . . , the common ratio is 3. If you present
the first term as t1, using the pattern above, you have,
1st term = t1
2nd term = t2
3rd term = t3
th
4 term = t4
5th term = t5
6th term = t6
Therefore, organizing the pattern, you have the number of terms and expressions for
the nth term as follows:
1st term = t1
2nd term = t2
3rd term = t3
th
4 term = t4
5th term = t5
6th term = t6
nth term = tn
2 · 3 0 = t1
2 · 31 = t1 r1
2 · 32 = t1r2
3
2 · 3 = t1r3
2 · 34 = t1 r4
2 · 35 = t1 r5
2 · 3n-1 = t1 rn-1
You will notice that the exponent of the common ratio is 1 less than the number of terms
you are looking for.
So, if you are looking the 3rd term, the exponent of the common ratio is 2; for the 4th
term, the exponent of the common ratio is 3; for the 6th term, the common ratio is 5,
etc…
Therefore, for the nth term, the exponent of the common ratio is n – 1, where n is the
number of terms.
To find the nth term of a geometric sequence, the formula is
tn = t1 rn-1
where n = the number of terms
r = common ratio
t1 = first term
tn = last term
So, if you want to find the 10th term of the sequence 2, 6, 18, 54, 162, . . . , then you
have to use the formula for convenience tn = t1 rn-1.
First identify the given before you substitute to the formula:
t1 = 2
r =3
n = 10
tn = ?
first term
common ratio
number of terms
the term you are looking for
Solution:
tn = t1 rn-1
t10 = 2 (3)10 -1
t10 = 2 (3)9
t10 = 2 (19,683)
t10 = 39,366
Substitute the given value
Simplify the exponent
Simplify(3)9 . It is equal to 19, 683
Therefore the 10th term of the sequence 2, 6, 18, 54, 162, . . . is 39,366.
LET US PRACTICE!
A. Find the next four terms of the sequence.
1.
1 1
, , 1, 2, . . .
4 2
2. -
1 1
, , -1, 2, . .
4 2
3. 32, -16, 8, -4, . . .
4. -
1
1 1 1
,- ,- ,- , ..
32 16 8 4
5.
2 , 2, 2 2 , 4, . . .
6.
1 1 1
, , , 1, . . .
27 9 3
7. -1, 4, -16, 32, . . .
8. 12, 24, 48, 96, . . .
9. 10, 2,
2 2
,
,...
5 25
10. 7, 14, 28, 56, . . .
LET US DO IT!!
Tell whether or not each number sequence is a geometric sequence. Those that are
geometric, give the common ratio.
a. 6, 24, 96, 384, . . .
b. 5, -10, 20, -40, . . .
c.
1
, 1, 2, 4, . . .
2
d. 3, 9, 27, . . .
e. 2, 4, 6, 8, 10, . . .
f.
1
,1, 3, 9, . . .
3
g. 7, 9, 11, 13, . . .
h. 15, 5,
5 5
, ,...
3 9
1
,...
2
i.
4, 2, 1,
j.
3, 7, 11, 15, . . .
Given the following sequences, tell which are geometric and which are arithmetic
sequences. State their common ratio or common difference.
k. 5, 20, 80, 320, . . .
l.
1, 4, 9, 16, . . .
m. 3, 8, 13, 18, . . .
n. 1, 4, 9, 16, . . .
o. 31, 38, 45, 52, . . .
p. 4, 12, 36, 108, . . .
q. 1, -3, 5, -7, . . .
r. 1, 6, 36, 216, . . .
s.
1 2 3 4
, , , ,...
2 3 4 5
2 3 4 5
, , ,
,...
1 4 9 16
B. Write the first five terms of the geometric progression where
t.
1. a1 = 2,
2. a1 = 3,
r=3
r=2
1
3. a1 = 10, r =
2
1
4. a1 = 32, r =
4
5. a1 = 3, r = -2
6. a1 = 2, r = -3
2
1
7. a1 = , r = 3
2
8. a1 = 1, r = 0.5
9. a1 = -1, r = 0.5
10. a1 = -2, r = -2
_____________________
Math Teacher
Parent’s Name/Signature
Name: _________________________________ Grade and Section: ______________
School: __________________________________
Date: _____________________
LEARNING ACTIVITY SHEET
Mathematics 10
Week 6 – 1st Quarter
This learning activity sheet provides varied activities that will help you solve
problems involving arithmetic and geometric sequences.
At the end of this learning activity sheet, the learners are expected to:
 solve problems involving sequences. (M10AL–If–2)
Directions: Using the nth term of the arithmetic and geometric sequence, solve the
following items. Write your answer on the space provided.
1. The 20th term of the arithmetic sequence 5, 13, 21,29, 37,…
2. The 15th term of an arithmetic sequence whose a1 = 12 and whose d = - 9.
3. The 13th term of the geometric sequence whose first term is 3 and whose
common ratio is -2.
4. The 8th term of the geometric sequence whose a1 = -4 and whose r = 3.
5. The 24th term of the arithmetic sequence whose first term is 25 and whose
common difference is -6.
Directions: Decode the tagline set by the Department of Health in line with its
program “Fight CoViD – 19” by solving the following problems involving sequences.
Write the word that corresponds to each answer on the space provided below to complete
the tagline.
at
Flatten
Always
6
15 days
13 days
Stay
to
curve
2
7
78732
the
circle
home
60
6132
3
A country struck by the Corona Virus Disease – 19 (CoViD19) reached its peak infecting
81,920 people in total. It was found that the virus spread is in a Geometric Progression and that
the number of people infected gets doubled each day reason for its government to implement a
total lockdown. If there were only 5 people infected on the first day, how many days had passed
to reach its peak?
1
2
After a knee surgery, your trainer tells you to return to your jogging program slowly. He
suggests jogging for 12 minutes for the first week. Each week thereafter, he suggests you to
increase the time by 6 minutes. How many minutes will you need after the 9th week?
3
A microbiologist was able to isolate 12 endophytic bacterial strains from nipa palm in
Bulacan, Philippines. In this study, screening of endophytic bacteria examined their multiple plant
growth-promoting traits. These bacteria are able to increase their numbers by the process of
replication called binary fission whereby their population triples every generation time. Find the
total population (sum) of bacteria after 9 generation time?
4
The common ratio on item number 1.
5
The common difference on item number 2.
6
The common ratio of item number 3.
Tagline:
1
20
30
40
50
60
Directions: Solve the following problems involving sequences. Write your answer
on the space provided. *Show your complete solution.
1. An auditorium has 10 seats in the first row and 4 additional seats in each
successive row. How many seats will be there on the 18th row?
2. Kristine used her savings to buy a new car amounting to Php720,000.00. Suppose a
car’s value depreciates yearly at 10%, what is her car’s value after 4 years?
3. A side of an apartment building is shaped like a steep staircase. The windows
are arranged in columns. The first column has 2 windows, the second column has 5
windows, the next has 8, then 11, and so on. How many windows are on the side of the
apartment if there are 15 columns?
4. Assuming that the geometric sequence continues, what is the height of a
bouncing ball on its 8th bounce if its initial height after the first drop is 140 ft., next is 70
ft., and so on?
5. Determine the seating capacity of a gymnasium with 18 seats on the first row,
20 on the second, 22 on the third. The sequence of the seating capacity per row continues
until the 14th row.
Solution:
Reference/s:
Callanta, Melvin; Canonigo ,Allan, et. al.: Grade 10 Mathematics Learner’s Module.
Edited by Maxima Acelajado, Ph. D. Pasig City, Philippines. DEPED-IMCS Rex Book
Store, Inc. 2015.
_____________________
Math Teacher
Parent’s Name/Signature