LEARNING MODULE

Mathematics 10
10
Quarter 1
Self-Learning Module 3
Finding the Sum of the Terms of
a Given Arithmetic Sequence

 MELCs-aligned

 Integrates 4S of
learning
 TABLE OF CONTENTS
PAGE
WHAT THIS MODULE IS ABOUT
Note to the Teacher/Facilitator iii
Note to the Learner iii
Note to the Parents/Guardian iii
How to Learn from this Module iv

Parts of the Module with 4S Learning Model Components iv

WHAT I NEED TO KNOW (LEARNING OUTCOMES) vi

WHAT I KNOW (Pre-test) vi

REVIEW vii

LESSON: Sum of Arithmetic Sequence and its Notation Symbol. 1

Activity 1 6
Activity 2 7
Activity 3 8
Activity 4 11

WRAP-UP 11

POST TEST 12

ANSWER KEY 13

REFERENCES 14
What this Module is About

Welcome to the Mathematics Grade 10 Self-Learning Module on finding the sum of the
terms in a given arithmetic sequence.
This Self-Learning Module was designed and developed by the researcher and reviewed by
selected experts from Department of Education who handled Mathematics subjects. The writer/s utilized
the standards set by the K to 12 Curriculum using the Most Essential Learning Competencies (MELC)
in developing this instructional resource.

Module Developers: Paul John E. Calam (researcher) and Dr. Maria Antonieta A. Bacabac (adviser)

This learning material hopes to engage the learners in guided and independent learning
activities at their own pace and time. Further, this material is guided with the 4S Learning Cycle model,
namely: Sense making, Showing of representation, Solution and explanation, and Summarization. Also
aims to help learners acquire the needed 21st-century skills while taking into consideration their needs
and circumstances.

In addition to the material in the main text, you will also see this box in the body of the self-
learning module:

Notes to the Teacher

This contains helpful tips or strategiesthat
will help you in guiding the learners.

Notes to the Teacher/Facilitator:

As a facilitator you are expected to orient the learners on how to use this module. You also need
to keep track of the learners' progress while allowing them to manage their own learning.
Furthermore, you are expected to encourage and assist the learners as they do the tasks included
in the module.
Notes to the Learner:
Welcome to the Mathematics 10 Self Learning Module on finding the sum of the terms in a given
arithmetic sequence or the Arithmetic Series.
This self- learning module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to process the
contents of the learning material while being an active learner.
How to Learn from this Module

To achieve the objectives in this self-learning module, you are to do the following:
1. Take your time reading the lessons carefully.
2. Follow the directions and/or instructions in the activities and exercises diligently.
3. Answer all the given tests and exercises.

Parts of the Module with 4S Learning Model Components

4S Learning Model Parts of the

Purpose
components Definition Modules

This point to the set of

knowledge and skills that
Learning students should acquire
Outcomes after completing the
module.
This is a pre-test
assessment as to your level
of knowledge to the
Pretest subject matter at hand,
meant specifically to
gauge prior related
knowledge
Refers This refers to students’ ability to
turn circumstances into a situation
that is comprehended clearly by Review of Prior This part connects previous
Sense-making using their prior knowledge and Knowledge lesson with that of the
experience to explain the given current one.
problem.

This section discusses the

Lesson
lessons for the students to
understand the concept.
 This is an activity where
This refers to students’ ability to students will be given an
illustrate the model to opportunity to illustrate the
Showing communicate mathematical ideas model to communicate
Representation through the use of manipulative Activity 1 mathematical ideas through
materials, diagrams, graphical the use of manipulative
displays, or symbolic materials, diagrams,
expressions. graphical displays, or
symbolic expressions.
Refers to accurate response This is an activity where
Solving with through the algorithm with students will solve and
Explanation clarity and justification why the Activity 2 explain their solutions.
answer to the question is correct.
This is an activity where a
Refers to the students’ ability to
put together the concept student put together the
Synthesizing discussed in their own words, in Activity 3 concept discussed in their
a simple manner and correct own words, in a simple
context manner and correct context.

This is an activity where

Sense-making, students will solve word
Showing problems by applying the
Representation, Activity 4 4S(Sense-making, Showing
Solving with Representation, Solving
Explanation and with Explanation and
Synthesizing Synthesizing) method of
problem solving.

This section summarizes

Synthesizing Wrap-up the concepts and
application of the lesson.
This evaluates your level
Posttest of mastery in achieving the
learning objectives.

At the end of this module you will also find:

References This is a list of all sources used in developing this module.

The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the module.
Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer the Pretest before moving on to the other activities included in
the module.
3. Read the instruction carefully before doing each task.
 4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not hesitate to consult
your teacher or facilitator. Always bear in mind that you are not alone.
We hope that through this material, you will experience meaningful learning and gain deep
understanding of the relevant competencies. You can do it!

Learning Outcomes

This Module is divided into 2 lessons;

1 – Sum of Arithmetic Sequence and It’s Notation Symbol
– Solving Problems in Finding the Sum of Arithmetic Sequence

At the end of this module, you should be able to:

1. determines arithmetic means, nth term of an arithmetic sequence and sum of
terms of a given arithmetic sequence. (M10AL-Ib-2)
You will also be expected to:
a. define arithmetic series.
b. Illustrates the sum of the terms in a given arithmetic sequence.
c. differentiate arithmetic series and arithmetic sequence.
d. provide the arithmetic series expressed by a summation notation.
e. derive the formula in finding the sum of the terms of the given
arithmetic sequence.
f. compute the sum of the terms of the given arithmetic sequence.
g. solve problems involving sum of a given arithmetic sequence.
h. show appreciation on the concept of arithmetic series in a real life
situation.

PRETEST

Directions: Identify what is being asked in each question. Write your answer in your paper.

1. What is the sum of the eight term of an arithmetic sequence whose 𝑎3 =

7 and 𝑎5 = 11?
A. 48 B. 80 C. 104 D. 168
2. What is the sum of all odd numbers from 1 to 50?
A. 625 B. 637.5 C. 1250 D. 1275
3. Which of the following does not illustrate arithmetic sequence?
 A. natural numbers B. even numbers C. prime numbers D. odd numbers
4. Which of the following represents the arithmetic series of the multiples of 3
between 9 and 30?
A. 9 + 15 + 18 + 21 + 24 + 27 + 30 B. 9,18,27
C. 15 + 18 + 21 + 24 + 27 D. 15 + 18 + 21 + 24 + 27 + 30
5. If the sum of the arithmetic series is 690, the first term is 19 and the last term is
96, how many terms are there in a sequence?
A. 9 B. 10 C.11 D.12
6. What is the sum of the numbers between 1 and 100 which are divisible by 6?
A. 714 B. 816 C. 917 D. 918
7. What is the sum of the first 20 terms in an arithmetic sequence whose first term
is -122 and the common difference is 9?
A. −4150 B. −730 C. 730 D. 4150
8. Ms. Covie spends her time during home quarantine in a legit online business
selling RTW items. During the first week of her business, she receives 7 orders
from 7 costumers. In the second week, her 7 costumers and 5 new costumers
order items she is selling. Amazingly in the third week of her business, another
5 added in her costumer’s list who also order items weekly. If this patterns
continue, how many items Covie sold in the entire eight week of her business.
A. 19 B. 35 C. 42 D. 43
9. Which of the following is the first 5 terms of an arithmetic sequence whose 𝑆𝑛 =
966, 𝑎1 = 17 and 𝑎𝑛 = 121?
A. 25,33,41,49,57 B. 17,22,27,32,37 C. 17,25,33,41,49 D. 17,20,23,26,29
10.Grade 10 students are tasked to form a triangular pyramid out from 400 blocks.
How many layers of blocks can be made if there are 39 blocks in the bottom
and only 1 block at the top of the pyramid?
A. 10 B. 15 C. 20 D. 25

REVIEW
A. Can you fill in the Blank?

Consider this sequence:

3 __ __ __ 23

a. How will you able to find the missing term? __________________________

b. What type of sequence is illustrated above? _________________________
c. Can you give the definition of the sequence? _________________________
d. What is the concept used in finding the missing term? __________________
 Do you still remember the concept of arithmetic mean which was discussed in the previous lesson? If you
have forgotten take a look on the previous lesson to refresh the concept so that in the next discussion there will
be no confusion in your mind about the concept arithmetic sequence, arithmetic mean and arithmetic series.
Review the concept and proceed to the next activity.

B. Similar but Different

3,8,13,18,23 3 + 8 + 13 + 18 + 23
Figure 1 Figure 2

a. What have you observed? _______________________________________

b. What is similar in figure 1 and figure 2? ______________________________
c. What is different in figure 1 and figure 2? _____________________________
d. What operation is involved in figure 2? _______________________________

Does the activity help you identify the similarities and differences of arithmetic sequence and arithmetic
series? How will you differentiate the two figure? If nothing bothers you, let’s now have a brief discussion on
arithmetic sequences and arithmetic series.

Illustrations
1. 3, 8, 13, 18, 23 This is an arithmetic sequence.
3 + 8 + 13 +18 +23 If you wish to find the sum of an arithmetic
sequence it is now called as arithmetic series.

2. 16, 10, 4, −2, −8 Arithmetic Sequence

16 + 10 + 4 − 2 − 8 Arithmetic Series

LESSON

Series is an indicated sum of terms in a sequence. 1,2,3,4,5,6,7,8,9,10 is an arithmetic sequence, this follows
that 1+2+3+4+5+6+7+8+9+10 is an arithmetic series. Arithmetic series refers to the sum of the terms in a
given arithmetic sequence. 𝑆𝑛 is a notation used for arithmetic series, where 𝑆 is for sum and 𝑛 is for the first
nth term. The summation notation is also used to express arithmetic series.
 𝑆𝑛 𝑆3 𝑆10

Sum of the first 3 terms Sum of the first 10 terms

Sum of the first nth terms

The Summation/Sigma Notation

Sigma notation is used to express the sum of an arithmetic series more easily and conveniently.
Like the series 2 + 4 + 6, +8, +10, + … + 20 it can be expressed as

. “The sum of 2n as n goes from 1 to 10”, this is how the expression be read. Study the

illustration that follows.

Last val ue of n
The formula in getting the terms of the
sequence

Firstvalue of n

Notation use for Finding the Sum

Remember
of the Terms in a Given Arithmetic Sequence

There are two Notation we can use to present the sum arithmetic
series:
i. ( 𝑆𝑛 ) the sum of the nth termand;
ii. ∑ Sigma or the summation symbol.
 In this part of the Module you will be learning on how to interpret the sum of the terms in a given
arithmetic sequence which was expressed in the two notation symbol. In the later part, you will be asked to
express the given arithmetic series in its notation symbol.

Remember Sum of term inArithmetic Sequence

The formula in getting the sum of an arithmetic series are;
𝒏
i. 𝑺𝒏 = ( 𝒂𝟏 + 𝒂 𝒏 ) where; 𝑛 is the number of terms
𝟐
𝑎 𝑛 is the last term
𝑎1 is the first term
𝒏
ii. 𝑺 𝒏 = ( 𝟐𝒂 𝟏 + ( 𝒏 − 𝟏 )𝒅 if 𝑎 𝑛 is unknown, where𝑑 is the
𝟐
common difference

Example 1. In the Arithmetic Sequence 1, 2, 3, 4, 5, …, find 𝑆10 .

Solution: Explanation
𝑆10 Write what is asked in the problem.
𝑆10 = 1 + 2 + 3 + 4 + 5+6 + 7 + 8 + 9 + 10 𝑆10 means the sum of the first 10 term of the
sequence. In the sequence, the first 10 terms
are 1,2,3,4,5,6,7,8,9,10 and we simply add
the terms to express its sum.
𝑆10 = 55 Add all the numbers from 1 to 10.

Therefore: 𝑆10 or the sum of the first 10 terms in the sequence is 55.

Example 2. In the Arithmetic Sequence 1, 2, 3, 4, 5, … ,100, find 𝑆20 .

Solution: Explanation
𝑆20 Write what is asked in the problem.
𝑆20 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 𝑆20 means the sum of the first 20 term of the
13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 sequence. In the sequence, the first 20 terms
are
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
and we simply add the terms to express its sum.
𝑆20 = 210 Add all the numbers from 1 to 20.

Therefore: 𝑆20 or the sum of the first 20 terms in the sequence is 210.
Example 3. Find the sum of the arithmetic series expressed by .

Solution: (To find the sum of the arithmetic series expressed by sigma notation above, find the 10
terms first using the term formula where n start from 1 up to 10.)

This is the term formula in the problem.

Step 1. Find the first term

7𝑛 − 5 Write the formula of the terms in the problem.
7(1) − 5 Substitute 1 for n since we want to find the 1st term.
7−5 Multiply 7 and 1.
2 Subtract 7 and 5.
Therefore 𝑎1 is 2.
Step 2. Find the second term
7𝑛 − 5 Formula of the terms in the problem.
7(2) − 5 Substitute 2 for n since we want to find the 2nd term.
14 − 5 Multiply 7 and 2.
9 Subtract 14 and 5.
Therefore 𝑎2 is 9.
Step 3. Using the first 2 terms, identify the common difference to find remaining 8 terms.
(𝑑 = 𝑠𝑢𝑐𝑐𝑒𝑑𝑖𝑛𝑔 𝑡𝑒𝑟𝑚 − 𝑝𝑟𝑒𝑐𝑒𝑒𝑑𝑖𝑛𝑔 𝑡𝑒𝑟𝑚)
𝑑 = 𝑎2 − 𝑎1 Use the common difference formula.
𝑑=9−2 Substitute 9 to 𝑎2 and 2 to 𝑎1 .
𝑑=7 Subtract 9 and 2.
Therefore 7 is the common difference.
Step 4. Write out all the 10 terms of the sequence. Use the values of the first term 2, second term 9 and the common
difference 7.
2, 9, 16, 23, 30, 37, 44, 51, 58, 65
Step 5. Write the corresponding arithmetic series and find the sum.
2 + 9 + 16 + 23 + 30 + 37 + 44 + 51 + 58 + 65 = 335

Therefore: is equal 335.

Example 4. Find the sum of the first 15 even numbers and express it in summation notation.

Solution: Explanation
To solve the problem, identify the 15 even numbers
first before getting its sum.
2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 First 15 even numbers.
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16+18 + 20 + 22 + 24 + 26 + Its corresponding series. Add all 15 numbers
28 + 30 = 240
(To find its summation notation use your knowledge in
getting the general formula of an arithmetic sequence.)

𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑 General formula of an arithmetic sequence

𝑎𝑛 = 2 + (𝑛 − 1)2 Since the first term is, then 𝑎1 = 2 and their
common difference (d) is 2
𝑎𝑛 = 2 + 2𝑛 – 2 Substitute the values of first term and common
difference d
𝑎𝑛 = 2𝑛 By combining like terms

The sum of the first 15 even numbers is equivalent to

Therefore, = 240.

Example 5. Find the sum of the first 20 terms in the sequence whose 𝑎1 = −5 and 𝑑 = 3.
Solution: Explanation
Sum formula if 𝑎𝑛 is unknown.
Substitute 𝑛 = 20, 𝑎1 − 5 𝑎𝑛𝑑 𝑑 = 3.

𝑆20 = 10[2(−5) + (19)3] To get, divide 20 by 2 and subtract 20 by 1.

𝑆𝑛 = 10 (−10 + 57) To get, multiply 2 and −5 & 19 and 3.
𝑆𝑛 = 10 (47) To get, add −10 and 57.
𝑆𝑛 = 470 To get, multiply 10 and 47.

Therefore: The sum of the first 20 terms in the sequence is 470.

Example 6. In the arithmetic sequence 8, 14, 20, 26, 30, 34, …, which term is 122?

Solution: Explanation
Find n when 𝑎 𝑛 = 122 What is asked on the problem.
Let 𝑎1 = 8, 𝑑 = 6, and 𝑎 𝑛 = 122 Assumptions based on the given.
𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑 General formula of an arithmetic sequence
122 = 8 + (𝑛 − 1)6 Substitute the known quantities
122=8+6n – 6 Apply the distributive property

120=6n By combining like terms

n = 20 Divide both sides by 6

Thus, 122 is the 20th term.

Are the examples clear to you? If you have some confusions and questions in mind don’t hesitate to
ask your teacher or your facilitator for clarification. You can also ask your classmate or friends for
help in understanding the concept that is unclear to you. If you don’t have problem with the topic you
may now proceed to the next section.

ACTIVITIES

Read and analyze. Write your complete solution and explanation.

ACTIVITY 1: LET’S ILLUSTRATE!

Examine how the figures below are formed.

Figure 1 Figure 2 Figure3 Figure 4

a. Complete the table below using the given figures. Look for a pattern and then create the next three figures.
New number of coins
Figure Number Term Number Number of Coins minus previous number
of coins
1 1 1 -
 2 2 4 4–1=?
3 3
4 4
5 5
6 6
7 7
b. Complete Column 4.
c. Write the numbers in Column 3 in ascending order.
d. Find the common difference between any two consecutive terms in the sequence.
e. Explain your answers.

ACTIVITY 2: LET’S PRACTICE!

I. Provide the arithmetic series described in each item and explain the process.
Consider the sequence 1,2,3,4,5,6,7,8,9, … ,100
1. 𝑆5 3. 𝑆25 5. 𝑆56 7. 𝑆88 9. 𝑆95
2. 𝑆15 4. 𝑆70 6. 𝑆80 8. 𝑆77 10. 𝑆100
II. Provide the arithmetic series expressed by the summation/sigma notation below and explain the process.

1. 4.

2.

3. 5.
 ACTIVITY 3. SYNTHESIZING
Answer each of the following.
1. How do you define arithmetic series?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
________________________
2. Compare and contrast arithmetic series and arithmetic sequence using a Venn
diagram.

3. In your own words, why is there a need to use 𝑆𝑛 and ∑ notation to express the sum of
the terms in a given arithmetic sequence or the arithmetic series?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________

ACTIVITY 4. LET’S APPLY!

Solve the following problems below using the concepts you have learned about finding the sum of the terms in a given
arithmetic sequence. Provide complete solution incorporating the components of 4S learning model.

Problem 1: A mosaic in the shape of an equilateral triangle is 25 feet on each side. Each tile in the mosaic is
in the shape of an equilateral triangle, 12 inches to a side. The tiles are to alternate in color. How
many tiles of each color will be needed?
 I. Sense-making
1. Review Prior Knowledge
3,8,13,18,23 3 + 8 + 13 + 18 + 23
Figure 1 Figure 2

a. What have you observed? _______________________________________

b. What is similar in figure 1 and figure 2? ______________________________
c. What is different in figure 1 and figure 2? _____________________________
d. What operation is involved in figure 2? _______________________________

2. Questions for posted problem

1. What are the data needed in order to determine the number of tiles of each color
needed?

2. How will you find the number of tiles of each color needed?

II. Showing Representations

a. Draw the mosaic that is described in the problem.

b. Construct a table that shows the condition of the problem.

III. Solving with Explanation

 Write the formula to solve the problem. Why are you using the formula?

 Solve the problem and explain where you get the value of the variables
you substitute in the formula.

IV. Synthesizing
 1. Discuss the mathematical concepts applied to solve the problem.

Problem 2. A conference hall has 20 rows of seats. The first row contains 20 seats, the second row contains 22 seats,
the third row contains 24 seats, and so on. How many seats are there in the last row? How many seats are
there in the conference hall?

I. Sense-making
1. Review Prior Knowledge
a. What is a sequence? _______________________________________
b. What is the difference between a sequence and a series? ______________________________
c. Provide an example of a sequence and a series to illustrate their differences. ______________

2. Questions for posted problem

1. Based on the initial data given, is the number of seats from first to third row increases?
Or decreases? Is there a common difference as the number or seats by row changes?

2. What are the data needed in order to determine the total number of seats?

3. How will you find the number of seats in the conference hall?

II. Showing Representations

c. Illustrate the given scenario.

d. Construct a table that shows the condition of the problem.

III. Solving with Explanation

 Write the formula to solve the problem. Why are you using the formula?

 Solve the problem and explain where you get the value of the variables
you substitute in the formula.

IV. Synthesizing
2. Discuss the mathematical concepts applied to solve the problem.
 WRAP-UP

This module covers the lesson on arithmetic series and how they are illustrated in real life
situations. You learned to:
1) define arithmetic series;
2) illustrate the sum of the terms in a given arithmetic sequence;
3) differentiate arithmetic series from arithmetic sequence;
4) provide the arithmetic series expressed by a summation notation;
5) derive the formula in finding the sum of the terms of the given arithmetic sequence
6) compute the sum of the terms of the given arithmetic sequence
7) solve problems involving sum of a given arithmetic sequence
8) show appreciation on the concept of arithmetic series in a real life situation

Summary of the Formula

Use to find the sum of the terms in a given
arithmetic sequence when the first term the last
term and n are provided in the problem

Use to find the sum of the terms in a given

arithmetic sequence when the last term is
unknown.

POSTTEST
Directions: Identify what is being asked in each question. Show your complete solution with
explanation on each problem. Write your answer in your paper.

1. If the sum of the arithmetic series is 690, the first term is 19 and the last term is
96, how many terms are there in a sequence?
A. 9 B. 10 C.11 D.12
2. What is the sum of the eight term of an arithmetic sequence whose 𝑎3 =
7 and 𝑎5 = 11?
A. 48 B. 80 C. 104 D. 168
3. Which of the following does not illustrate arithmetic sequence?
A. natural numbers B. even numbers C. prime numbers D. odd numbers
 4. What is the sum of the numbers between 1 and 100 which are divisible by 6?
A. 714 B. 816 C. 917 D. 918
5. What is the sum of all odd numbers from 1 to 50?
A. 625 B. 637.5 C. 1250 D. 1275
6. Which of the following represents the arithmetic series of the multiples of 3
between 9 and 30?
A. 9 + 15 + 18 + 21 + 24 + 27 + 30 B. 9,18,27
C. 15 + 18 + 21 + 24 + 27 D. 15 + 18 + 21 + 24 + 27 + 30
7. What is the sum of the first 20 terms in an arithmetic sequence whose first term
is -122 and the common difference is 9?
A. −4150 B. −730 C. 730 D. 4150
8.Grade 10 students are tasked to form a triangular pyramid out from 400 blocks.
How many layers of blocks can be made if there are 39 blocks in the bottom
and only 1 block at the top of the pyramid?
A. 10 B. 15 C. 20 D. 25
9. Ms. Covie spends her time during home quarantine in a legit online business
selling RTW items. During the first week of her business, she receives 7 orders
from 7 costumers. In the second week, her 7 costumers and 5 new costumers
order items she is selling. Amazingly in the third week of her business, another
5 added in her costumer’s list who also order items weekly. If this patterns
continue, how many items Covie sold in the entire eight weeks of her business.
A. 19 B. 35 C. 42 D. 43
10. Which of the following is the first 5 terms of an arithmetic sequence whose 𝑆𝑛 =
966, 𝑎1 = 17 and 𝑎𝑛 = 121?
A. 25,33,41,49,57 B. 17,22,27,32,37 C. 17,25,33,41,49 D. 17,20,23,26,29

KEY TO CORRECTION
Activity 1:

The sequence is 1, 4, 7, 10, 13, 16, 19. The common difference is 3.

Activity 2:
I.
1. 1+2+3+4+5 = 15 6. 1+2+3+…+80 = 3240
2. 1+2+3+…+15 = 120 7. 1+2+3+…+88 = 3916
3. 1+2+3+…+25 = 325 8. 1+2+3+…+77 = 3003
4. 1+2+3+…+70 = 2485 9. 1+2+3+…+95 = 4560
5. 1+2+3+…+56 = 1596 10. 1+2+3+…+100 = 5050

II.
1. 5+7+9+11+13+15+17+19
2. 4+5+6+7+8+9+10+11
3. -2-4-6-8-10-12-14-16
4. 3+6+9+12+15+18+21+24+27+30+33+36+39+42+45
5. 6+2-2-6-10-14-18-22-26-30

Activity 3:
Answer may vary
Activity 4:
Answer may vary

Pretest Posttest
1. b 1. d
2. d 2. b
3. c 3. c
4. b 4. b
5. d 5. d
6. b 6. b
7. b 7. b
8. a 8. c
9. c 9. a
10. c 10. C

References
Amper, P. (2020). Module 1: Finding the sum of the Terms of a Given Arithmetic Sequence.
Department of Education (Region 10). Alternative Delivery Modality

Hazewinkel, Michiel, ed. (2001) [1994], "Arithmetic series", Encyclopedia of Mathematics, Springer
Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
https://en.wikipedia.org/wiki/Arithmetic_progression

Oronce, O., & Mendoza, M. (2015). E-MATH: Worktext inMathematics. Rex Book Store, Inc., page
26-31.
RD Sharma Solutions for Class 10 Maths Chapter 9 Arithmetic Progressions 2020, accessed on June
2020.https://byjus.com/rdsharma-solutions/class-10-maths-chapter-9-arithmeticprogressions/

Simmons, Bruce. 2020. “Arithmetic Series” Copyright © 2000 by Bruce Simmons. Updated July 9, 2017
by Mathworlds, accessed on June 2020. https://www.mathwords.com/a/arithmetic_series.htm

Schmitz, Andy. 2012. “Intermediate Algebra: Sequences and Series”.

https://saylordotorg.github.io/text_intermediate-algebra/s12-02arithmetic-sequences-and-serie.html

Wolfram Math World “The web’s most extensive mathematics resource”. Accessed on June 2020.
https://mathworld.wolfram.com/ArithmeticSeries.html