GENERATING PATTERNS AND ILLUSTRATING ARITHMETIC …

Module 1: Generating Patterns and Illustrating Arithmetic Sequence

10

Mathematics First Quarter – Module 1

GENERATING PATTERNS

AND ILLUSTRATING

ARITHMETIC SEQUENCE

𝒂𝒏 𝒂𝟏

𝒅

𝒏

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Mathematics - Grade 10

Alternative Delivery Mode

Quarter 1 – Module 1: Generating Patterns and Illustrating Arithmetic Sequence

First Edition, 2020

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Published by the Department of Education

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Office Address: IPHO Bldg. Sudlon, Lahug, Cebu City

Telefax: (032) 255 - 6405

Email Address: [email protected]

Development Team of the Module

Writer: Roy R. Flores

Editor: Jimjun F. Ramas

Reviewers: Dr. Anecita U. Mendez (Moderator)

Mr. Carmelito M. Lauron Sr.

Illustrator and Layout Artist: Myrna P. Soco

Management Team

Schools Division Superintendent:

Dr. Marilyn S. Andales, CESO V

Assistant Schools Division Superintendents:

Dr. Cartesa M. Perico

Dr. Ester A. Futalan

Dr. Leah B. Apao

Chief, CID: Dr. Mary Ann P. Flores

EPS in LRMS: Mr. Isaiash T. Wagas

EPS in Math: Dr. Pamela A. Rodemio

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10

Mathematics

First Quarter – Module 1:

GENERATING PATTERNS

AND ILLUSTRATING

ARITHMETIC SEQUENCE

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Introductory Message

This module is carefully designed to continually facilitate learners to

achieve mastery on the Most Essential Learning Competencies and develop their

21st century skills. This module consists of essential components developed

appropriately for self-instructional mode of learning. The components come in

various developmental purposes that are designed to diagnose (pretest), recall

and associate (review), discuss, explain and even provide practice activities,

enrichment tasks, assessments and answer keys.

Upon taking the pretest, determine whether you need to take or skip this

module. At 100% accuracy, you possess the mastery of the topic in the module;

hence, you don’t need to take it and you may choose to proceed to the next

module. At 99% and below, you are recommended to undertake the module to

acquire the necessary skills.

Though allowed, adult supervision is limited only to providing assistance

in accomplishing this module. It is highly recommended that YOU, the learner,

should try to engage independently in doing the different tasks for you to become

a critical thinker and problem solver which are the twin goals of Mathematics.

May this module be utilized to its fullest extent in the purpose of learning

the competencies construed as Most Essential for a learner in this level.

God bless and enjoy learning!

PAMELA A. RODEMIO Education Program Supervisor - MATH

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Grade 10 Mathematics

1

MOST ESSENTIAL LEARNING COMPETENCY:

generates patterns (M10AL-Ia-1)

illustrates an arithmetic sequence (M10AL-Ib-1)

Patterns and sequences can be applied in almost all aspects of our lives. We just

have to analyze how it can be used in our day-to-day life. Having knowledge about this lessons

can give us a different perspective on how things happen in our lives.

In this lesson, the learner:

generates pattern of a given sequence

finds the next few terms of a sequence

illustrates an arithmetic sequence

differentiates finite from infinite sequence

identifies the rule of a given arithmetic sequence

determines the common difference of an arithmetic sequence

writes the next few terms of an arithmetic sequence

solves problems involving arithmetic sequence with patience

relates patterns and sequences to real-life situations

GENERATING PATTERNS AND ILLUSTRATING ARITHMETIC SEQUENCE

What I Need To know

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What I know

Directions: Find out how much you already know about the topics in this module.

Choose the letter of the correct answer and write your answers on a separate sheet of

paper. Take note of the items that you were not able to answer correctly and find the

right answer as you go through this module.

1. What is the next term of the sequence 5z, 8x, 11v,…?

A. 14u B. 14t C. 15s D. 15r

2. Which of the following is an infinite sequence?

A. 1, 2, 3, 4,…5 B. 2, 4, 8, 16, 32,… C. 20, -15, 10, - 5, 0 D. 6, 2, -2, - 4, - 10

3. The pattern of a certain sequence is “divided by 3”. Which of the following

sequences follows the pattern?

A. 81, 27, 9, 3, 1 B. 1, 3, 27, 81 C. 3, 6, 9, 12, 15 D. 12, 9, 6, 3, 0

4. Which of the following completes the sequence ___, 2, 4, 6, 8, ___, 12?

A. 0 and 10 B. 0 and 14 C. 2 and 10 D. 2 and 12

5. What must be true about an arithmetic sequence whose common

difference is negative?

A. All the terms in the sequence are positive.

B. All the terms in the sequence are negative.

C. All the terms in the sequence are increasing.

D. All the terms in the sequence are decreasing.

6. Give the common difference of the arithmetic sequence 2, - 5, - 12, - 19.

A. – 7 B. 3 C. 7 D. – 3

7. Which of the following has a constant difference?

A. 1, 2, 3, 5, 8 B. 64, 32, 16, 8, 4 C. -10, - 6, - 2, 2, 6 D. -2, 4, -8, 16, -32

8. Which rule is applied in getting the values of a in the table below?

A. a = n + 1 B. a = 2n C. a = 𝑛2 D. a = n + 2

9. One of the sequences below is NOT an arithmetic sequence. Which one is it?

A. 9, 7, 5 , 3, 1 B. 0, - 3, - 6, 9, 12 C. – 1, - 2, - 3, - 4,- 5 D. ½, 1, 1½, 2, 2 ½

10. Find t so that 3t + 2, 4t + 3, 6t form an arithmetic sequence.

A. 4 B. – 4 C. 5 D. – 5

n 1 2 3 4 5

a 1 4 9 16 25

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11. The common difference of an arithmetic sequence is 1 4⁄ . If the first term is 1 2⁄ , find

the 11th term.

A. 13

4 B. 2 C. 2

1

4 D. 3

12. A pile of logs has 24 in the first layer, 23 in the second, 22 in the third, and so on.

How many logs are there in the 10th layer?

A. 16 B. 15 C. 14 D. 13

13. Rona started her blog last April 1, 2020. On her first week she had 8 followers, on

the second week she had 15, on the third week she had 22. If her followers grew

consistently, how many followers did she have on the 15th week?

A. 95 B. 100 C. 103 D. 106

14. After a knee surgery, your trainer told you to return to your jogging program slowly.

He suggested jogging for 12 minutes each day for the first week. Each week

thereafter, he suggested that you increase that time by 6 minutes per day. How many

weeks will it be before you can jog 1 hour per day?

A. 8 weeks B. 9 weeks C. 10 weeks D. 11 weeks

15. Henry started working in 2009 at an annual salary of Php 50 000 and received and

increment of Php 15 000 each year. In which year did his annual income reach

Php 200 000?

A. 2016 B. 2017 C. 2018 D. 2019

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What’s In

What is the next figure in each group?

What is your basis to get the next figure?

Is there a pattern to determine what comes next?

Task 1.

Given the following sets of numbers, observe the elements and answer the questions that follow.

Set A: {160, 80, 40, 20, 10…}

Are the numbers written in specific order?

What is the next number?

Give the pattern.

Set B: {1, 3, 9, 27, 81}

Is there a relationship among the elements of the set?

If we will add another number, what is it?

Give the pattern.

Spot the difference(s) between set A and set B.

What comes next?

a) , , , , d) 2, 4, 8, 16, ____

b) A, D, G, J, ______ e) , , , _____

c) 18, 14, 10, 6, _______

What’s New

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What is It

Task 2.

Below are squares formed by matchsticks.

Count the number of matchsticks in each figure and record the results in a table.

Answer the following.

1. Did you see a pattern on the number of matchsticks used?

2. Is there a constant increase in the number of matchsticks? By how much?

3. Complete the table without actual counting the number of matchsticks.

4. How did you determine the next numbers to complete the table?

In the first task, the next number in set A is 5 and the pattern is “divided by

2”. In set B, the next number is 243 and the pattern is “multiplied by 3”. The set of

numbers 160, 80, 40, 20, 10… and 1, 3, 9, 27, 81 are called sequences. A sequence

is usually associated with a pattern or a rule in order to generate the next terms.

“Divided by 2” and “multiplied by 3” are examples of a rule or pattern of a sequence.

Sequences are separated into two groups. A finite sequence contains a finite

number of terms (with first and last term) while infinite sequence contains an infinite

number of terms (with first term but no indicated last term). The three dots mean to

continue forward in the pattern established without limit. In task 1, set A is infinite while

set B is finite.

Number of squares 1 2 3 4 5 6 7 8 9 10

Number of matchsticks

Definition:

A sequence or progression is a list of numbers written in a specified order that

follows a definite pattern or rule. Each number in the sequence is called term. The

first number is called first term, followed by second term and so on.

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In general, the terms of a sequence are written as a1, a2, a3, a4, a5,…, an where

n represents the term position or number of terms. For example, a3 is the third term,

a5 is the 5th term and an is the nth term.

Sometimes a sequence is expressed as equation relating the nth term (an)

and the number of terms (n). Study this the following tables.

Table 1.

The table shows that the equation of the sequence 1, 4, 9, 16, 25,… is an = n2.

This equation can be written in words as: “The nth term of a sequence is the square

of the number of terms”. So if 10th term is unknown, we solve this way:

𝑎10 = 102 or 100

Table 2.

The table shows that the equation of the sequence 3, 6, 9, 12,… is an = 3n

This can be translated as: “The nth term of the sequence is thrice the number of

terms”.

So if the 12th term is unknown, we get: a12 = 3(12) or 36.

Finite Sequence Infinite Sequence

1, 1, 2, 3, 5 2, 6, 10, 14, …

18, 15, 12, 9,…- 6 1,1

2,1

4,1

8, …

√2, 2, 2√2, 4 -5, 10, -20, 40,…

n 1

(a1) 2

(a2) 3

(a3) 4

(a4) 5

(a5) …

n (an)

an 12 = 1 22 = 4 32 = 9 42 = 16 52 = 25 … n2

No. of Terms (n)

1 (a1)

2 (a2)

3 (a3)

4 (a4)

… n

(an)

nth Term (an)

(3x1) = 3 (3x2) = 6 (3x3) = 9 (3x4) = 12 … 3n

Remember:

To generate the next terms of a sequence, study the given terms and search for

the pattern or rule. It could be squaring, adding, subtracting, multiplying, dividing or a

combination of operations.

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In the second task, the complete table is shown below.

Notice that the number of matchsticks 4, 7, 10, 13, ….31 is a sequence whose

pattern is “plus 3” or “increased by 3”. This means that to get the next term of the

sequence we have to increase the preceding term by 3. Take note also that when

we subtract any preceding term from the next term the difference is constant.

7 − 4 = 𝟑, 10 − 7 = 𝟑, 13 − 10 = 𝟑, 16 − 13 = 𝟑 and so on.

In this case, 3 is the constant difference known as common difference or d.

Sequences with a common difference are called arithmetic sequence.

In general, the common difference (d) of an arithmetic sequence

𝑎1, 𝑎2, 𝑎3, 𝑎4, … 𝑎𝑛 is given by the formula 𝒅 = 𝒂𝒏 − 𝒂𝒏−𝟏 where 𝒂𝒏 is the last term

and 𝒂𝒏−𝟏 is the previous term.

If the common difference between consecutive terms is positive, we say that

the sequence is increasing and when the difference is negative we say that the

sequence is decreasing.

Number of squares 1 2 3 4 5 6 7 8 9 10

Number of matchsticks 4 7 10 13 16 19 22 25 28 31

Definition:

An arithmetic sequence or progression is a sequence where every term after

the first is obtained by adding a constant called the common difference (d).

Remember:

To generate the terms of an arithmetic sequence, we take the current term and

add the common difference to get to the next terms.

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What’s More

(Note: Use a whole sheet of paper to answer activities A to F.)

A. Independent Activity 1

Directions: Write F if the sequence is finite or I if the sequence is infinite.

1. 2, 3, 4, 5, …, 10

2. 7, 10, 13, 16, 19, 22, 25

3. 4, 9, 14, 19, …

4. 2, 6, 18, 54

5. 3, 9, 27, 81, …., 729, …

B. Independent Assessment 1

Directions: Generate a sequence with five terms given the first term and the pattern.

1. Starts with 5 and the pattern is “add 3”

_____, _____, _____, _____, _____

2. The pattern is “divide by 2 ” and the first term is 480.

_____, _____, _____, _____, _____

3. The rule is “multiply by - 3” and starts from -12.

_____, _____, _____, _____, _____

4. The first term is 2 and the pattern is “multiply by 5 minus 7”.

_____, _____, _____, _____, _____

5. Starts with 112 and the pattern is “half of the current number plus 8”.

_____, _____, _____, _____, _____

C. Independent Activity 2

Directions: Match each sequence with its pattern. Write the letter only.

Sequence Pattern

1) 4, 11, 18, 25, … A. Multiply the previous term by 3.

2) 40, 20, 10, 5, … B. Divide the previous term by 2.

3) 100, 96, 92, 88, … C. One-third of the previous term.

4) 4, 12, 36, 108, … D. Add 7 to the previous term.

5) 81, 27, 9, 3 E. Subtract 4 from the previous term.

D. Independent Assessment 2

D.1. Directions: Give the common difference of the following arithmetic sequences.

1. 7, 14, 21, 28,…

2. 0.50, 0.35, 0.2, 0.05…

3. 10a + 5, 8a + 6, 6a + 7, 4a + 8

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D. 2. Directions: Given the value of d, write the next 3 terms of the sequence.

4. 24, ______, ______, ______ d = 11

5. 1

4, _____, ______, ______ d =

3

4

E. Independent Activity 3

Directions: Choose the letter corresponding to the correct answer.

1. Which of the following is the 10th term of the sequence 50, 42, 34, 26,….?

A. – 2 B. – 8 C. – 18 D. – 22

2. The pattern of a certain sequence is “triple it and subtract 15”. If the 2nd term is

45, what is the first term?

A. 15 B. 20 C. 25 D. 30

3. In the arithmetic sequence 1

2, 1,

3

2, 2,

5

2 , what is the common difference?

A. 1

2 B.

2

3 C.

1

4 D.

3

4

4. Given the sequence 4, 8, 12, 16, …, which of the following is the pattern or

rule that describes it?

A. multiply by 2 B. divide by 2 C. add 4 D. subtract 4

5. A sequence is defined by the equation an = 𝟏

𝟐𝒏 − 𝟓 where n is the number of

terms. Which one is the value of a10?

A. 5 B. 15 C. – 5 D. 0

F. Independent Assessment 3


1. Which of the following is an arithmetic sequence?

A. 1, 2, 3, 5, 8,.. B. 3, -9, 27, -81,... C. 24, 12, 6, 3,… D.1, - 6, -13, -20

2. Find the next two terms in the sequence – ½, - 5/6, - 7/6, ___, ___.

A. – 3/2, - 11/6 B. – 5/2, - 2 C. – 3/2, - 5/6 D. – 5/2, - 13/6

3. A sequence is defined by the equation an = 3n2. Find the 12th term.

A. 416 B. 432 C. 455 D. 467

4. The next term of a sequence is obtained by multiplying the previous term by

(- 5) then add 3. If the previous term is – 12, what is the next term?

A. – 20 B. 60 C. 63 D. – 57

5. Find m if m + 5, 4m + 1, and 6m form an arithmetic sequence.

A. 3 B. 4 C. 5 D. 6

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Answer the following.

(Note: Write your answers on a separate sheet of paper.)

A. Fill in the Blank.

Directions: Fill in the blanks with the correct word or words to make the statement

complete.

1. A ________ is a list of numbers written in a specified order that follows a definite pattern

or rule.

2. A sequence is also called _________.

3. Each number in the sequence is called _____.

4. _______ sequence contains a finite number of terms, while ________ sequence

contains an infinite number of terms.

5. In a sequence, n refers to _______ and an refers to ________. a1 means __________,

a2 means_________ and so on.

6. Sequence can also be expressed as a rule or _______ relating the nth term to the

number of terms.

7. ___________ is a sequence where every term after the first is obtained by adding a

constant called the _______________ (d).

8. If the common difference between consecutive terms of an arithmetic sequence is

________, we say that the sequence is increasing and when the difference is

________, we say that the sequence is decreasing.

9. To generate the terms of an arithmetic sequence, we take the current term and

_________ the __________ to get the next term.

10. If a1, a2, a3, a4,…an, is an arithmetic sequence, then an – an-1 is called __________.

B. True or False

Directions: Write T if the statement is TRUE and F if it is FALSE.

1. The next terms of a sequence cannot be determined by giving only the first 2 terms and

no other information.

2. If the first 3 terms of a sequence are given, then it can be examined as to whether it is

an arithmetic sequence or not.

3. If a sequence has a common difference, then it is an arithmetic sequence.

4. The sequence 1, 2, 3, 4, 5,… is a finite sequence.

5. If an is the 3rd term, then an-1 is the 2nd term.

11.

What I Have Learned

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What I can Do

Assessment

Apply what you have learned in this module by answering the following problems.

Directions: Solve the following problems and express your idea on the question that

follow. Use a separate answer sheet.

1. Ina made deposits from her school allowances as follows: P10 on

the first week, P13 on the second week, P16 on the third week and

so on, until she made 20 deposits. What was the amount of her last

deposit?

Why is saving money important? Explain.

2. Lhea is practicing her dance steps for the competition. She starts

practicing the steps for 1 hour on the first day and then increases

the practice time by 10 minutes each day. If the pattern continues,

how many hours will she spend practicing on the 13th day?

Is winning a competition every contestant’s goal? Why? Why not?

3. Old faithful is a natural geyser (at the Yellowstone National Park)

that produces long eruptions that are easily predictable and

surprisingly no one controls it. The time between eruptions is

based on the length of the previous eruption. If an eruption lasts

one minute, then the next eruption will occur in approximately 46

minutes. If an eruption lasts for 2 minutes then the next eruption

will occur in 58 minutes. If an eruption lasts for 3 minutes then the

next eruption will occur in 70 minutes and so on. If an eruption lasts

for 8 minutes, approximately in how many minutes the next

eruption occur?

As a concerned citizen, how can you help the government during

calamities?


1. If you are to write the next term of the sequence 12, 5, - 2, - 9,…what will

it be?

A. - 7 B. - 11 C. - 16 D. - 26

2. Which of the following is a finite sequence?

A. 1, 2, 3, 4,…5 B. 2, 4, 8, 16, 32,… C. 20, -15, 10, - 5, … D. 6, 2, -2, - 4, ...

3. The pattern of a certain sequence is “multiply by - 3”. Which of the following

sequences follows the pattern?

A. 81, 27, 9, 3, 1 B. -1, 3, -27, 81 C. 3, 9, 27, 81 D. -2, -6, -18, -54

4. Which of the following completes the sequence 64, ___, 16, 8, ___?

A. 42 and 2 B. 40 and 4 C. 32 and 6 D. 32 and 4

Image shows a cold water geyser

driven by carbon dioxide erupting

from an unplugged oil exploration

well drilled in 1936 into a natural

CO2 reservoir in Utah

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5. The first term of a sequence is 5. Which of the following patterns would make the

sequence arithmetic?

I. Add 4 to the previous term.

II. Multiply 4 to the previous term.

III. Subtract 4 from the previous term.

IV. Divide the previous term by 4.

A. I only B. I and II only C. I and III only D. II and IV on

6. Give the common difference of the arithmetic sequence 0.25, 0.4, 0.55, 0.7.

A. 0.65 B. 0.73 C. 0.81 D. 0.85

7. Which of the following has a constant difference?

A. 2, 6, 18, 54 B. 16, 25, 36, 49 C. -10, 6, 16, 20, 30 D. 35, 23, 11, - 1

8. Which rule is applied in getting the values of a in the table below?

A. a = n - 1 B. a = 2n - 3 C. a = 𝑛2- 1 D. a = 3n - 2

9. One of the sequences below is NOT an arithmetic sequence. Which one is it?

A. 9, 7, 5 , 3, 1 B. 0, - 3, 6, - 9, 12 C. – 1, - 2, - 3, - 4,- 5 D. ½, 1, 1½, 2, 2 ½

10. Find x so that x – 3, 4x + 7, x + 5,… form an arithmetic sequence.

A. 5 B. – 4 C. 3 D. – 2

11. The common difference of an arithmetic sequence is 1 2⁄ . If the first term is 1 4⁄ , find

the 7th term.

A. 23

4 B. 3 C. 3

1

4 D. 3

1

2

12. In the sequence 6, 13, 27, 55, …, each term after the first is determined by

multiplying the preceding term by m and then adding n. What is the value of n?

A. 1 B. 2 C. 3 D. 4

13. What is the next term of the sequence in item # 12?

A. 72 B. 87 C. 103 D. 111

14. Kevin is monitoring the growth of a seedling by measuring its height daily. He

noticed that the height of the seedling is increasing at a constant rate of 1.75 cm

per day. If the initial height of the seedling is 9.25 cm, in how many days would it be

25 cm long?

A. 8 days B. 9 days C. 10 days D. 11 days

15. At 3:25 PM, a car is running at a speed of 84 km/h at point A then decreases its

speed every minute by 12 km/h and stops at point B. At what time did the car stop

at B?

A. 3:30 PM B. 3:31 PM c. 3:32 PM d. 3:33 PM

n 1 2 3 4 5

a -1 1 3 5 7

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Something More:

Mrs. Perez bought a new kitchen appliance that costs

P15 000. She made an initial payment of P3 000.00 and

agreed to pay the remaining amount in 15 equal monthly

installments starting the following month.

a) Copy and complete the table below on your

answer sheet.

b) What kind of sequence did you get?

c) What amount represents the first term of the sequence?

d) What is the common difference of the sequence?

e) How much will be her remaining balance after one year?

No. of

months 0 1 2 3 4 5 6 7 8 9 10 11 12

Remaining

Balance

(in Pesos)

Additional Activity

Gas Range with Oven

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Key to Correction

WHAT I KNOW

1)B

2)B

3)A

4)A

5)D

6)A

7)C

8)C

9)B

10)A

11)D

12)B

13)D

14)B

15)D

WHAT’S MORE

A. Independent Activity 1

1)F

2)F

3)I

4)F

5)I

B. Independent Assessment 1

1)5, 8, 11, 14, 17

2)480, 240, 120, 60, 30

3)-12, 36, - 108, 324, - 972

4)2, 3, 8, 33, 158

5)112, 64, 40, 28, 22

C. Independent Activity 2

1)D

2)B

3)E

4)A

5)C

E. Independent Activity 3

1) D

2) B

3) A

4) C

5) D

F. Independent Assessment 3

1) D

2) A

3) B

4) C

5) A

D. Independent Assessment 2

1)7

2)0.15

3)(– 2a + 1) or (1 – 2a)

4)35, 46, 57

5)1, 5/4, 2

WHAT I HAVE LEARNED

A. Filling the Blank

1)Sequence 7) Arithmetic sequence , common difference

2)Progression 8) positive, negative

3)Term 9) add, common difference

4)Finite, infinite 10) common difference

5)number of terms, nth or last term, B. True or False

first term, second term 1) T 3) T 5) T

6)equation 2) F 4) F

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ASSESSMENT

1)C

2)A

3)B

4)D

5)C

6)D

7)D

8)B

9)B

10)D

11)C

12)A

13)D

14)B

15)B

WHAT CAN I DO

1)Php 67.00

Answers may vary

2)3 hours

Answers may vary.

3)130 minutes

Answers may vary.

ADDITIONAL ACTIVITY

a)

No. of months 0 1 2 3 4 5 6 7 8 9 10 11 12

Remaining

Balance

(in Pesos)

12000 11200 10400 9600 8800 8000 7200 6400 5600 4800 4000 3200 2400

b) arithmetic sequence

c) a1 = P12000.00

d) d = - 800

e) Php 2400.00

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REFERENCES AND WEBSITE LINKS USED IN THIS MODULE:

References:

“Intermediate Algebra” by Dilao, Soledad Jose. pp. 178-181.

Jala, L.L. (2011). “College Algebra”. (p. 185). Philippines

“Mathematics Learner’s Module Grade 10”. pp. 1 – 13.

Perez,I. Santos,L. et.al. (2016). “Interactive Mathematics”. (pp. 2-11). Philippines

Website Links:

Source: “Introduction to Arithmetic Sequences”, accessed June 15, 2020,

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b

61c86:

Source: “Arithmetic Sequence-Definition-and Basic Examples”, accessed June 28, 2020, https://www.chilimath.com/lessons intermediate-algebra

Source: “Arithmetic Sequences”, accessed July 2, 2020, https://www.katesmathlessons.com

Source: “Number Sequence Problems”, accessed July 9, 2020,

https://www.onlinemathlearning.com/number-sequence-problems.

Source: “Arithmetic Sequence Formula”, accessed July 9, 2020,

https://www.chilimath.com/lessons/intermediate-algebra/arithmetic-sequence-formula

For inquiries and feedback, please write or call:

Department of Education, Region VII, Division of Cebu Province

(Office Address) IPHO Bldg. Sudlon, Lahug, Cebu City

Telefax: (032) 255 - 6405

Email Address: [email protected]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:introduction-to-arithmetic-sequences/a/introduction-to-arithmetic-sequences

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:introduction-to-arithmetic-sequences/a/introduction-to-arithmetic-sequences

https://www.katesmathlessons.com/arithmetic-sequences.html

https://www.onlinemathlearning.com/number-sequence-problems.html

https://www.chilimath.com/lessons/intermediate-algebra/arithmetic-sequence-formula/

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