ARITHMETIC MEAN AND THE N TERM OF AN ARITHMETIC
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence10MathematicsFirst Quarter – Module 2ARITHMETIC MEAN ANDTHE Nth TERM OF ANARITHMETIC SEQUENCE
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceMathematics - Grade 10Alternative Delivery ModeQuarter 1 – Module 2: Arithmetic Mean and the nth Term of an Arithmetic SequenceFirst Edition, 2020REPUBLIC Act 8293, section 176 states that No copyright shall subsist in any work of theGovernment of the Philippines. However, prior approval of the government agency or officewherein the work is created shall be necessary for exploitation of such work for profit. Such agencyor office may, among other things impose as a condition the payment of royalties.Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,trademarks, etc.) included in this book are owned by their respective copyright holders. Everyeffort has been exerted to locate and seek permission to use this materials from their respectivecopyright owners. The publisher and authors do not represent nor claim ownership over them.Published by the Department of EducationSecretary: Leonor Magtolis BrionesUndersecretary: Diosdado M. San AntonioDevelopment Team of the ModuleWriter: Roy R. FloresEditor: Jimjun F. RamasReviewers: Dr. Anecita U. Mendez (Moderator)Mr. Carmelito M. Lauron Sr.Illustrator and Layout Artist: Myrna P. SocoManagement TeamSchools Division Superintendent:Dr. Marilyn S. Andales, CESO VAssistant Schools Division Superintendents:Dr. Cartesa M. PericoDr. Ester A. FutalanDr. Leah B. ApaoChief, CID:Dr. Mary Ann P. FloresEPS in LRMS: Mr. Isaiash T. WagasEPS in Math: Dr. Pamela A. RodemioPrinted in the Philippines by:Department of Education, Region VII, Division of Cebu ProvinceOffice Address: IPHO Bldg. Sudlon, Lahug, Cebu CityTelefax: (032) 255 - 6405Email Address: cebu.province@deped.gov.ph
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence10MathematicsFirst Quarter – Module 2:ARITHMETIC MEAN ANDTHE Nth TERM OF ANARITHMETIC SEQUENCE
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceIntroductory MessageThis module is carefully designed to continually facilitate learners toachieve mastery on the Most Essential Learning Competencies and develop their21st century skills. This module consists of essential components developedappropriately for self-instructional mode of learning. The components come invarious developmental purposes that are designed to diagnose (pretest), recalland 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 thismodule. 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 nextmodule. At 99% and below, you are recommended to undertake the module toacquire the necessary skills.Though allowed, adult supervision is limited only to providing assistancein accomplishing this module. It is highly recommended that YOU, the learner,should try to engage independently in doing the different tasks for you to becomea 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 learningthe competencies construed as Most Essential for a learner in this level.God bless and enjoy learning!PAMELA A. RODEMIOEducation Program Supervisor - MATH
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceARITHMETIC MEAN AND THE Nth TERM AND OF ANARITHMETIC SEQUENCEMOST ESSENTIAL LEARNING COMPETENCY: determines the mean of an arithmetic sequence finds nth term of an arithmetic sequenceWhat I Need To knowArithmetic sequences are used throughout mathematics and applied to engineering,sciences, computer sciences, biology and finance problems. The concepts of arithmetic meanand nth term of an arithmetic sequence can be applied in solving some real-life problems.This module will teach you how to deal with the nth term and the mean of an arithmeticsequence and apply them in solving problems in the real world. Go over the lessons and havefun in working with the exercises.In this lesson, the learner: inserts arithmetic mean(s) between two non-consecutive terms of anarithmetic sequencefinds the nth term of an arithmetic sequencelists down the first few terms of an arithmetic sequence given the generalterm and vice-versasolves word problems involving arithmetic meanapplies the concepts of mean and the nth term of an arithmetic sequence tosolve real-life problemsGrade 10 Mathematics1
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceWhat I knowDirections: 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 ofpaper. Take note of the items that you were not able to answer correctly and find theright answer as you go through this module.1. Find the arithmetic mean between – 13 and 25.A. – 14B. – 8C. 6D. 122. The first term of an arithmetic sequence is 3 and the common difference is - 7. Findthe 23rd term.A. – 151B. – 144C. – 137D. – 1303. If three arithmetic means are inserted between 11 and 39, find the second arithmeticmean.A. 18B. 25C. 32D. 464. Which term of the arithmetic sequence 4, 1, - 2, - 5 , . . . is - 29 ?A. 9th termB. 10th termC. 11th termD. 12th term5. What is the 7th term of the arithmetic sequence 14, 10, 6, 2, .?A. – 4B. – 5C. – 6D. – 106. 𝑚, 5𝑥 1, 𝑛 form an arithmetic sequence. If the common difference is 2x 1,what is 𝑚 equal to?B. 5x – 2A. 7x 3C. 5xD. 3x7. What is the nth term of the arithmetic sequence 7, 9, 11, 13, ?A. 𝑎𝑛 3𝑛 4.B. 𝑎𝑛 4𝑛 3.C. 𝑎𝑛 𝑛 2D. 𝑎𝑛 2𝑛 5.8. Find the value of c when the arithmetic mean of 𝑐 7 𝑎𝑛𝑑 𝑐 3 is 3𝑐 9.A. – 2B. – 3C. 2D. 39. If t 4 and 3t 2, 4t 3, 6t, form an arithmetic sequence, find the 9 th term.A. 34B. 44C. 54D. 6410. If a1 4 and d - 3, write the explicit formula of the arithmetic sequence.A. an 3n – 7B. an 7 – 3nC. an 7n – 3D. an 3 – 7n11. Find the next term of the sequence 2a – 5, 5a – 3, 8a – 1, 11a 1, A. 14a – 2B. 14 a – 3C. 14a 2D. 14a 312. The 5th term of an arithmetic sequence is 2 and the 11 th term is 20. Find the firstterm.A. – 10Grade 10 MathematicsB. – 9C. – 72D. – 4
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence13. Find the value of x if the arithmetic mean of 3 and 3x – 5 is 8.A. – 2B. – 4C. 5D. 614. 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 24 th layer?A. 1B. 2C. 3D. 415. A theater has 50 seats in the first row. Each row behind the first row gains twoadditional seats. How many seats are there in the 25th row?A. 86B. 90C.94D. 98What’s InAnswer the following.Given the arithmetic sequence87, 102, 117, 132, .a) Give the common difference.b) Write the next 3 terms.c) What number precedes (comes before) 132?d) What number is located in between 87 and 117?e) What numbers lie between 87 and 132?What’s NewActivity 1.Given a 4 - letter word with a corresponding number above each letter,811,2,5,rearrange the letters to form a new word such that the corresponding numberswill form an arithmetic sequence.a) What is the new word?b) What is the common difference of the sequence formed?Grade 10 Mathematics3
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequencec) What number is in between 8 and 2? 5 and 11?d) What numbers lie between 2 and 11?Activity 2.Consider the arithmetic sequence3, 7, , 15, , 23, 1. What is the pattern or rule for this sequence?2. Insert the two missing terms.3. What do you call number(s) in between two non-consecutive terms of anarithmetic sequence?4. Is there another way of getting the missing terms without using the commondifference?5. If you are to find the 150th term of the sequence without listing the previousterms, how would you do it?What is ItThe letters are arranged in this manner to form an arithmetic sequence.118,,5252,,8,11,The new word formed is MEAN and the arithmetic sequence is 2, 5, 8, 11, where d 3. 5 is the term in between 8 and 2 and 8 is the term in between 5 and 11.The two numbers that lie between 2 and 11 are 5 and 8.In the given sequence is 3,7, 11, 15, 19, 23, The rule is “increased by4”. Therefore the missing terms are 11 and 19. These 2 numbers are called arithmeticmeans. 11 is the arithmetic mean of 7 and 15 and 19 is the arithmetic mean of 15 and23.Definition:Let us consider again the given sequence in Activity 2.The term or terms between any two non-consecutive terms of an arithmeticsequence is called arithmetic mean.Grade 10 Mathematics4
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence11193, 7, ,15, ,23, abmLet a and b be the two non-consecutive terms of the sequence and m be themean as shown above.Observe the following illustration.A.B.𝟕 𝟏𝟓𝟐 𝟏𝟓 𝟐𝟑𝟐𝟐𝟐 𝟐 𝟏𝟏𝟑𝟖𝟐 𝟏𝟗What can you deduce from the illustration?Remember:If a, m, b form an arithmetic sequence then:𝒎 𝒂 𝒃𝟐Illustrative Example:Problem: The arithmetic mean between 2 numbers is -15. If one number is 17, findthe other number.Solution:Let b the other number𝒎 𝒂 𝒃𝟐 𝟏𝟓 𝟏𝟕 𝒃𝟐(Substitution)17 𝑏 15(2)(Multiplication Property)17 𝑏 30(Multiplication)𝑏 30 17(Addition Property)𝑏 47(Addition)Therefore, the other number is (- 47).Inserting 2 or more arithmetic means between two non-consecutive terms ofan arithmetic sequence is tricky. For example, if we want to insert 4 arithmetic meansGrade 10 Mathematics5
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequencebetween 15 and 55, we have to consider first their common difference (d). Althoughwe can do this by inspection or trial and error method, but it is important to use theproper method to find the value of d because this is useful to solve other problemsinvolving arithmetic sequence like the last question in Activity 2.To find the common difference of an arithmetic sequence, we will use the nthterm formula.In general, the first n terms of an arithmetic sequence with a1 as the first termand d as the common difference are𝑎1 , 𝑎1 𝑑, 𝑎1 2𝑑, . 𝑎1 (𝑛 1)𝑑If a1 and d are known, then any term in an arithmetic sequence is easy to findusing the rule𝒂𝒏 𝒂𝟏 (𝒏 𝟏)𝒅Where:𝒂𝒏 last term𝒂𝟏 first term𝒏 number of terms𝒅 common differenceIllustrative Example 1:Problem: Insert 4 arithmetic means between 15 and 55.Step 1: Write the sequence using blank for the missing terms. (15, a2, a3, a4, a5, 55).Step 2: Identify the given and unknown data in the problem.Given:𝑎1 15 (first term), 𝑎𝑛 55 (last term) and 𝑛 6 (the no. of terms)(Note: n 2 given terms 4 arithmetic means 6)Unknown: common difference (𝑑)Step 3: Substitute the given values using the formula then solve.𝑎𝑛 𝑎1 (𝑛 1)𝑑55 15 (6 – 1) d(Substitution)55 15 5d(Simplification)55 - 15 5d(Addition Property)40 5d(Subtraction)d 8 (common difference)(Multiplication Property)Grade 10 Mathematics6
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceTo complete the sequence, we will add 8 to the preceding term to obtain the nextterms. Therefore, the 4 arithmetic means between 15 and 55 are 23, 31, 39 and 47.Illustrative Example 2:Problem: Find the 150th term of the sequence 3, 7, 11, 15, .Solution:Given: a1 3, d 4, n 150Unknown: a150Plug the given values into the formula and solve.𝒂𝒏 𝒂𝟏 (𝒏 𝟏)𝒅𝑎150 3 (150 1)4𝑎150 3 (149)4𝑎150 3 (596)𝑎150 599Therefore, the 150th term is 599.Illustrative Example 3:Problem: Give the nth term formula of the arithmetic sequence 11, 9, 7, 5, 3, Solution:Given: a1 11 and d - 2Unknown: nth term formula or anBy plugging the given values, we get:𝒂𝒏 𝒂𝟏 (𝒏 𝟏)𝒅𝑎𝑛 11 (𝑛 1)( 2)(Substitution)𝑎𝑛 11 2 2𝑛(Distributive Property)𝒂𝒏 𝟐𝒏 𝟏𝟑 or 𝒂𝒏 𝟏𝟑 𝟐𝒏Therefore, the nth term of 11, 9, 7, 5, 3, is 𝒂𝒏 𝟐𝒏 𝟏𝟑 or 𝒂𝒏 𝟏𝟑 𝟐𝒏.Remember:Equations in the form of 𝒂𝒏 𝒅𝒏 𝒄 is called the explicit formula of anarithmetic sequence where d is the common difference and c is constant. An explicitformula designates the nth term of the sequence as an expression of n where n isthe term's location. It defines the sequence as a formula in terms of n.Grade 10 Mathematics7
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceWhat’s MoreA. Independent Activity 1(Use a whole sheet of paper to answer activities A to F.)Directions: Directions: Compute the arithmetic mean between the following pairs ofnumbers.1. 475 and 6152. 8 and – 123.23and344. 𝑥 3 and 3𝑥 15. 2 5 and 6B. Independent Assessment 1Directions: Insert the indicated number of arithmetic means between the given terms.1. 2 and 38[2]2. 58 and (– 2)[3]1and 2[4]4. ( 5) and 11[3]5. (𝑥 𝑦) and (4𝑥 2𝑦)[2]3.3C. Independent Activity 2Directions: Write the first 5 terms of the arithmetic sequence given the general nthterm.1. 𝑎𝑛 10𝑛2. 𝑎𝑛 7𝑛 23. 𝑎𝑛 𝑛 54. 𝑎𝑛 4 3𝑛15. 𝑎𝑛 𝑛 12Grade 10 Mathematics8
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceD. Independent Assessment 2Directions: Give the general nth term of the following arithmetic sequences.1. 15, 24, 33, 42, 2. - 8, - 3, 2, 7, 3. 4, - 3, - 10, - 17, 4. 0, 1.5, 3, 4.5, 5.14,12,34, 1, E. Independent Activity 3Directions: Read the problems carefully and choose the letter of the correct answer.1. Which of the following is the arithmetic mean of 3𝑥 2 𝑎𝑛𝑑 15𝑥 2 ?A. – 6XB. – 9XC. – 6X2D. – 9X22. Insert 3 arithmetic means between 11 and – 13.A. -5, -2, 1B. 5, -1, -7C. 4, 0, -4D. 6, 0, -613. What is the 20th term of sequence defined by 𝑎𝑛 2 𝑛 3?A. 21B. 23C. 13D. 74. Which term of the arithmetic sequence 2, 11, 20, 29 is 101 ?a. 10thb. 11thc. 12thd. 13th5. If 𝑎3 38 𝑎𝑛𝑑 𝑎9 4, find 𝑎10 .A. – 7B. – 11C. – 15D. – 17F. Independent Assessment 3Directions: Choose the correct answer. Write the letter only.1. What is x if the arithmetic mean of 25 and 3x is 17.A. – 4C. – 2B. 3D. 52. Write the explicit formula of the sequence 5, 14, 23, 32, 41, .A. 𝑎𝑛 9𝑛 5B. 𝑎𝑛 9𝑛 2C. 𝑎𝑛 9𝑛 4D. 𝑎𝑛 9𝑛 33. Find the value of n if 5𝑛 2 is the arithmetic mean of 2𝑛 3 𝑎𝑛𝑑 6𝑛 1.A. 4C. – 2B. 3D. 54. The 16th term of an arithmetic sequence is 48. If the common difference is 3,find the first term.A. 3B. 2C. 1D. - 15. Given two terms in the arithmetic sequence, a5 - 8 and a25 72, find theequation for the nth term.A. A. 𝑎𝑛 5𝑛 2Grade 10 MathematicsB. 𝑎𝑛 4𝑛 289C. 𝑎𝑛 3𝑛 27 D. 𝑎𝑛 2𝑛 35
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceWhat I Have LearnedAnswer the following.(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 statementcomplete.1. The term or terms between any two non-consecutive terms of an arithmetic sequenceis called .2. If the first term and the common difference of an arithmetic sequence are given, thenthe nth term can be determined using the formula .3. 𝑎𝑛 𝑑𝑛 𝑐 is known as the formula of an arithmetic sequence whered is the .4. If a, m, b forms arithmetic sequence, then m is called .5. The first step in inserting 2 or more arithmetic means between non-consecutive termsof an arithmetic sequence is to find the value of .B. True or False.Directions: Write T if the statement is TRUE and F if it is FALSE.1. Half of the sum of the two non-consecutive terms of an arithmetic sequence will giveus the arithmetic mean.2. If 𝑎𝑛 10𝑛 15 is the explicit formula of an arithmetic sequence, then – 15 is thecommon difference.3. Given the value of the first term and the last term of an arithmetic sequence, thecommon difference can be determined.4. If the explicit formula of an arithmetic sequence is known, then we can generate theterms of the sequence.5. We can determine the nth term of an arithmetic sequence given the first term and thecommon difference without listing the previous terms.Grade 10 Mathematics10
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceWhat I can DoApply what you have learned in this module by answering the following real-lifeproblems.Directions: Use a separate answer sheet to answer the following problems.1. The number of Covid-19 positive cases in a certain areawas found to be increasing at an average rate of 2 personsper day. There were 3 Covid-19 positive cases at the start.a) How many positive cases will there be after 2 weeks?b) Why do you think the number of Covid-19 patients isincreasing?c) As a concerned citizen of this country, what can you doto minimize the spread of the virus?2. Jean invests P1000 on October 1, 2015 to October 1, 2022.The investment earns 8% per annum simple interest, paidevery October 1st of the year.a) How many years did he invest his money? What is n?b) How much is the increase of his money every year?c) Complete the table 022Hint: Simple Interest Principal x Rate x Timed) Determine the value of the investment on October 1, 2022.e) What is the difference between saving money in a bank and keeping it as cash inyour house?Grade 10 Mathematics11
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceAssessmentDirections: On your answer sheet, write the letter corresponding to the correctanswer.1. If five arithmetic means are inserted between -9 and 9, what is the third mean?B. – 3A. 3C. 0D. 62. Find the arithmetic mean between 35 and - 9.A. – 22B. 13D. – 12C. 153. The first term of an arithmetic sequence is 6 and the common difference is 19. Findthe 17th term.A. 300B. 305C. 307D. 3104. Which term of the arithmetic sequence 7, 22, 37, . . . is 112 ?A. 7th termB. 8th termC. 9th termD. 10th term5. In an arithmetic sequence, a 3 8 and a7 24. What is the common difference?A. 6B. 5C. 4D. 36. 𝑎, 3𝑥 2, 𝑏 form an arithmetic sequence. If the common difference is 2x - 1, whatis 𝑎 equal to?A. x 3B. 5x 1C. 3x - 1D. 2x 37. What is the nth term of the arithmetic sequence 10, 16, 22, 28, ?A. 𝑎𝑛 6𝑛 4.B. 𝑎𝑛 6𝑛 3.C. 𝑎𝑛 6𝑛 2D. 𝑎𝑛 6𝑛 4.8. If w - 2 and 2w - 1, w 1, w 5, , form an arithmetic sequence, find the 10 th term.A. 27B. 31C. 35D. 399. If a1 - 3 and d 2, write the explicit formula of the arithmetic sequence.A. an 5n 2C. an 2n – 5B. an 5n - 2D. an 2n 510. The common difference of an arithmetic sequence is 3 2. If the first term is 2 2 , findthe 42nd term.A. 125 2B. 123 2C. 121 2D. 115 211. Find the missing term of the arithmetic sequence 253, 58, , - 332, .A. – 195B. – 137C. – 132thD. – 12912. The 4 term of an arithmetic sequence is 17 and the 9 term is 32. Find the 14th term.A. 42thB. 45C. 46D. 4713. Find the value of y if the arithmetic mean of – 2 and 4y is 6.A. – 3Grade 10 MathematicsB. 7/2C. - 512D. 3/2
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence14. Due to Covid-19 pandemic the number of online sellers in a certain town increasesevery week. On the first week, there were only 6 online sellers and after 4 monthsthere were already 51 of them. If the increase of the number of sellers per week isconstant, what is the increase per week?A. 6B. 5c. 4D. 315. The value of a certain machinery product decreases by P15 000 every year. If theproduct was originally priced at P450 000, find its selling price after 7 years.A. P375 000B. P360 000C. P345 000D. P330 000Additional ActivityDirections: Read and interpret the problem carefully then answer the questions thatfollow. Write your answers on a separate sheet of paper.Rings in the cross-section of a tree trunk can be used toestimate the age of a tree. The width of the rings varied fromyear to year due to variations in annual growing conditions.However, the average width of one ring was found to be 9 mm.In 2001, the radius of the trunk was 63 mm (not including thebark). Several years later, a second measurement of the radiuswas taken and found to be 198 mm.1.2.3.4.What kind of sequence is involve in this problem?What number represents the first term? last term?What number represents the common difference?Since the year of the first measurement is given and the year of the secondmeasurement is unknown, which element of the arithmetic sequence ismissing? (first term, last term, number of terms, common difference)5. Assuming that the average width of each ring is 9 mm.a) In what year the second measurement was taken?b) How old was the tree during that year? Show your solutions usingthe nth term formula of an arithmetic sequence.Grade 10 Mathematics13
14WHAT’S MOREWHAT I KNOWC9)A8)D7)D6)D5)D4)B3)A2)C1)10) B11) D12) A13) DGrade 10 MathematicsA. Independent Activity 1D. Independent Assessment 21. 𝑎𝑛 9𝑛 61) 5452) – 22. 𝑎𝑛 5𝑛 133. 𝑎𝑛 7𝑛 113) 17/244) 2x 1𝑎𝑛4. 1.5𝑛 1.515) 5 35. 𝑎𝑛 𝑛4B. Independent Assessment 11) 14, 26E. Independent Activity 31. C2) 43, 28, 132. B3) 2/3, 1, 4/3, 5/33. D4) – 1, 3, 74. C5) 2x, 3x - y5. B14) A15) DC. Independent Activity 2F. Independent Assessment 31) 10, 20, 30, 40, 501. B2) 5, 12, 19, 26, 332. C3) 6, 7, 8, 9, 103. A4) 1, - 2, - 5, - 8, - 114. A5) 3/2, 2, 5/2, 3, 7/25. BWHAT I HAVE LEARNEDA. Filling the BlankB. TRUE OR FALSE1. arithmetic mean1. T2. 𝑎𝑛 𝑎1 (𝑛 1)𝑑2. F3. explicit formula, common difference3. F4. arithmetic mean4. T5. common difference5. TKey to CorrectionModule 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence
Grade 10 Mathematics15ASSESSMENTWHAT CAN I DO1) C1) a) 292) Bb) Answers may vary.3) Dc) Answers may vary.4) A2) a) 7 years, n 85) Cb) P80.006) Ac)7) 020140020211480202215608) B9) C10) A11) Bd) P1560.0012) De) Answers may vary.13) B14) D15) CADDITIONAL ACTIVITY1. arithmetic sequence2. a1 63, a2 1983. 9 mm4. Number of terms (n)5. a) 2017b) 16 years old𝑎𝑛 𝑎1 (𝑛 1)𝑑198 63 (𝑛 1)9198 63 9𝑛 9198 54 9𝑛9𝑛 144𝑛 16Module 2: Arithmetic Mean and the NthTerm of an Arithmetic Sequence
Module 2: Arithmetic Mean and the NthTerm of an Arithmetic SequenceREFERENCES AND WEBSITE LINKS USED IN THIS MODULE:References:“Intermediate Algebra” by Soledad Jose-Dilao. pp.178-181Jala, L.L., .(2011). “College Algebra”. p.185, Philippines“Mathematics Learner’s Module Grade 10”. pp. 14 - 15Perez,I., Santos,L., et.al. (2016). “Interactive Mathematics”. (pp. 2-11), Philippines:Website Links:Source: “Arithmetic Sequences”, accessed July 2, equencesSource: “Arithmetic Sequence Formula”, accessed July 9, e-algebra/arithmetic-sequence-formula/Source: “Sequence Strategy”, accessed July 21, ct/dm.Source: “Arithmetic Sequence Word Problems”, accessed July 21, 2020https://www.youtube.com/watch?v TXLHkRnzBR0Source: “Real-life-Problems Involving Arithmetic Series”, accessed July 22, 2020https://www.onlinemath4all.comFor inquiries and feedback, please write or call:Department of Education, Region VII, Division of Cebu Province(Office Address) IPHO Bldg. Sudlon, Lahug, Cebu CityTelefax: (032) 255 - 6405Email Address: cebuprovince@deped.gov.phGrade 10 Mathematics16
arithmetic sequence finds the nth term of an arithmetic sequence lists down the first few terms of an arithmetic sequence given the general term and vice-versa solves word problems involving arithmetic mean applies the concepts of mean and the nth term of an arithmetic sequence
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3.2 Arithmetic series: the sum of an arithmetic sequence Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. 7C 7D Arithmetic Sequence Arithmetic Series 6C 6D Arithmetic sequences Arithmetic series 3.1 3.2 Arithmetic sequence Arithmetic s
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The first course, Section 4B75, is Python Programming (1/7/19 – 2/11/19), the second course, Section 4B83, is Big Data Analysis & Visualization (2/11/19 – 3/25/19), and the last course in the series, Section 4B84, is Unix Operating Systems (3/25/19 – 4/29/19). In Python and Unix, it is assumed students have no knowledge of programming or computing. All of these courses will use data sets .
