Math 10 Geometric Sequences and Means PDF

Math 10 EVM Ma’am Hanie Banzuelo Quarter 2 Week 4 – 2nd Meeting SCAN FOR ATTENDANCE  Weekly Instructional Schedule for Week 4 WEEK MEETING NO. NO. EXPECTED ACTIVITIES/TASKS Discussio...

Math 10 EVM Ma’am Hanie Banzuelo Quarter 2 Week 4 – 2nd Meeting SCAN FOR ATTENDANCE  Weekly Instructional Schedule for Week 4 WEEK MEETING NO. NO. EXPECTED ACTIVITIES/TASKS Discussion of Chapter & Unit Test Test 2.1: Arithmetic 1st Sequences, Series & Means 2nd T2.4. Geometric Sequence and Means 4 3rd T2.5. Geometric Series Bridge Day NMP Remediation - Translation and Writing Equations GRADE 10 MATHEMATICS_WEEKLY INSTRUCTIONAL SCHEDULE Second Quarter ❑ C.1.4. Illustrates a geometric sequence. ❑ C.1.5 Differentiates a geometric sequence from an arithmetic sequence. ❑ C.1.6. Determines geometric means, nth term of a geometric sequence. ❑ C.1.7. Solves problems involving sequences.  BACTERIA CULTURE A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be in 12 hours? GEOMETRIC SEQUENCE NUMBER OF HOURS TOTAL NUMBER (every 2 hours) OF BACTERIA A culture of Initial Time 500 bacteria doubles 2 1000 every 2 hours. 4 2000 If there are 500 bacteria at the 6 4000 beginning, how many 8 8000 bacteria will there 10 16000 be in 12 hours? 12 32000 GEOMETRIC SEQUENCE Geometric Sequence  GEOMETRIC SEQUENCE - Also known as “GEOMETRIC PROGRESSION”. - A sequence whose succeeding terms are produced by constantly multiplying the same number from the previous term to get the next term. The number multiplied to each term is known as the common ratio, and is denoted by the letter, r. 𝑛−1 𝑎𝑛 = 𝑎1 𝑟 no. of terms n th term common ratio 1 st term Learning Competency: C.1.4. Illustrates a geometric sequence.  GEOMETRIC SEQUENCE ~ Math for Innovative Minds 10, p. 25 Learning Competency: C.1.4. Illustrates a geometric sequence.  Determine whether the given are GEOMETRIC SEQUENCE or NOT. 1. 1, 2, 4, 8, 16 2. 80, -40, 20, -10, 5 3. 2, 6, -18, -54, 162 4. (x+y), (x+y)2, (x+y)3, (x+y)4, (x+y)5 Learning Competency: C.1.4. Illustrates a geometric sequence. ❑ C.1.4. Illustrates a geometric sequence. ❑ C.1.5 Differentiates a geometric sequence from an arithmetic sequence. ❑ C.1.6. Determines geometric means, nth term of a geometric sequence. ❑ C.1.7. Solves problems involving sequences.  Exercises: Answer the following questions. What is the 6th term of the geometric sequence whose 1st term is 3 and whose common ratio is -2. GENERAL RULE (an) 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 -6 , ___ 3, ___ 12 , -24 48 , ___ ___ , ___ -96 Multiplied by -2 (common ratio) CONCLUSION: The 6th term is -96. ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. GENERAL RULE (an) 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 CONCLUSION: The 4th term is -32. ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. What is the 7th term of the geometric sequence 2, 6, 18, 54, 162,…? GENERAL RULE (an) 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 CONCLUSION: The 7th term is 1458. ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. What is the 1st term of a geometric sequence GENERAL RULE (an) whose 2nd term is 20 and 6th term is 320? 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 ? , 20 , ___ , ___ , ___ , 320 ___ ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. What is the 1st term of a geometric sequence GENERAL RULE (an) whose 2nd term is 20 and 6th term is 320? 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 ? , 20 , ___ , ___ , ___ , 320 ___ Divide the 2 equations to solve for the common ratio (r). ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. What is the 1st term of a geometric sequence GENERAL RULE (an) whose 2nd term is 20 and 6th term is 320? 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 ? , 20 , ___ , ___ , ___ , 320 ___ Substitute the common ratio to solve for the 1st term. ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. What is the 1st term of a geometric sequence GENERAL RULE (an) whose 2nd term is 20 and 6th term is 320? 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 ? , 20 , ___ , ___ , ___ , 320 ___ ___ , 20 , ___ , ___ , ___ , 320 ___ , 20 , ___ , ___ , ___ , 320 ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence. Geometric Means  GEOMETRIC MEANS The terms between any two terms of a geometric sequence. ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  GEOMETRIC MEANS ~ Math for Innovative Minds 10, p. 28 ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. Think of a number between 3 and 75 GENERAL RULE (an) with a common ratio. 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 3 , ___ , 75 15 , 75 3 , ___ 3 , -15 ___ , 75 ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. Think of three numbers between GENERAL RULE (an) 1 and 16 with a common ratio. 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 1 , ___ , ___ , ___ , 16 2 , ___ 1 , ___ 4 , ___ 8 , 16 -2 , ___ 1 , ___ 4 , -8 ___ , 16 ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence.  Exercises: Answer the following questions. Think of two numbers between GENERAL RULE (an) 125 and 64 with a common ratio. 𝑎𝑛 = 𝑎1 𝑟 𝑛−1 125 , ___ 100 , ___ 80 , 64 ❑ Learning Competency: C.1.6. Determines geometric means, nth term of a geometric sequence. ❑ C.1.4. Illustrates a geometric sequence. ❑ C.1.5 Differentiates a geometric sequence from an arithmetic sequence. ❑ C.1.6. Determines geometric means, nth term of a geometric sequence. ❑ C.1.7. Solves problems involving sequences.  BACTERIA CULTURE A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be in 12 hours? ❑ Learning Competency: C.1.7. Solves problems involving sequences.  NUMBER OF HOURS TOTAL NUMBER (every 2 hours) OF BACTERIA Initial Time 500 2 1000 4 2000 6 4000 8 8000 10 16000 12 32000 ❑ Learning Competency: C.1.7. Solves problems involving sequences.  Exercises: Answer the following questions. Rein complain that the hot tub in the hotel suite is not hot enough. The hotel tells her that they will increase the temperature by 10% each hour. If the current temperature of the hot tub is 75ºF, what will be the temperature of the hot tub after 3 hours? ❑ Learning Competency: C.1.10. Solve problems involving Geometric, Fibonacci and Harmonic sequences.  Exercises: Answer the following questions. Rein complain that the hot tub in the hotel suite is not hot enough. The hotel tells her that they will increase the temperature by 10% each hour. If the current temperature of the hot tub is 75 ºF, what will be the temperature of the hot tub after 3 hours? AFTER THE 1ST HOUR AFTER THE 2ND HOUR AFTER THE 3RD HOUR 75ºF , _______ 90.75ºF , 99.825ºF 82.5ºF , _______ _______ + 7.5ºF + 8.25ºF + 9.075ºF 10% each hour 10% each hour 10% each hour ❑ Learning Competency: C.1.10. Solve problems involving Geometric, Fibonacci and Harmonic sequences.  Exercises: Answer the following questions. Rein complain that the hot tub in the hotel suite is not hot enough. The hotel tells her that they will increase the temperature by 10% each hour. If the current temperature of the hot tub is 75 ºF, what will be the temperature of the hot tub after 3 hours? AFTER THE 1ST HOUR AFTER THE 2ND HOUR AFTER THE 3RD HOUR 75ºF , _______ 90.75ºF , 99.825ºF 82.5ºF , _______ _______ 82.5 90.75 99.825 𝑟= = = = 1.1 = 110% 75 82.5 90.75 ❑ Learning Competency: C.1.10. Solve problems involving Geometric, Fibonacci and Harmonic sequences.  Exercises: Answer the following questions. Rein complain that the hot tub in the hotel suite is not hot enough. The hotel tells her that they will increase the temperature by 10% each hour. If the current temperature of the hot tub is 75 ºF, what will be the temperature of the hot tub after 3 hours? 75ºF , _______ 90.75ºF , 99.825ºF 82.5ºF , _______ _______ AFTER THE 1ST HOUR AFTER THE 2ND HOUR AFTER THE 3RD HOUR Since 𝒓 = 1.1 𝒏−𝟏 𝒂𝒏 = 𝒂𝟏 𝒓 𝑎4 = 75 (1.1)4−1 3 𝑎4 = 75 (1.1) 𝑎4 = 99.825ºF ❑ Learning Competency: C.1.10. Solve problems involving Geometric, Fibonacci and Harmonic sequences. Let’s answer some Textbook Exercises GEOMETRIC SEQUENCES Let’s discuss the Textbook Exercises pp. 43 - 47 Let’s discuss the Textbook Exercises pp. 43 - Let’s discuss the Textbook Exercises pp. 43 -  I understand … I need help… I need practice … I want more…  ervant Leadership ffective Communicator & Collaborator nalytical & Creative Thinker ife - long Learner Thomasian SEAL of Education SUSTAINABLE DEVELOPMENT GOALS