Download to read offline
More Related Content
Similar to Problem Solving in Arithmetic sequence.pptx
Problem Solving in Arithmetic sequence.pptx
- 1. What’s new! Suppose youparticipate in a bikeathon for charity. That charity starts with Php 50.00 in donations. Each participant must raise Php 200.00 in pledges. What is the minumum amount of money to be increased if there are 75 participants?
- 2. What’s the plan!Number of Participa nts (n) Total Amount Raised 1 50 2 250 3 450 … … 75 14,850 an = a1 + ( n-1) d a75 = 50 + (75-1) 200 = 50 + (74) 200 = 50 + 14,800 = 14, 850 To solve this problem, we'll calculate the total amount of money raised by the 75 participants, plus the initial donation. This forms an arithmetic sequence: 1.Initial donation: Php 50.00 2.Each participant raises: Php 200.00 3.Number of participants: 75 a1 = 50 n= 75 d= 200 Therefore, the minimum amount of money raised with 75 participants is Php 14, 850.00.
- 3. "Where Else Do WeSee Arithmetic Sequences in Daily Life?"
- 5.
- 6. solve real- life problems involving arithmetic sequences by applying theformula 2 OBJECTIVES 1 accurately and effectively write and solve arithmetic sequence problems; 3 appreciate the importance of arithmetic sequences in real- life contexts and demonstrate a positive attitude toward mathematical problem-solving.
- 7. Given a1 n d "GAS Up YourProblem-Solving!" Asked an=? Solution an = a1 + ( n-1) d
- 8. Example Problem: Bacterial Growth Ina scientific observation, a researcher notes a bacterial population growth pattern. Starting with 100 bacteria, the population increases by 50 every hour. This scenario serves as an effective illustration of an arithmetic sequence
- 9. A scientist isobserving the growth of bacteria in a petri dish. The initial population is 100 bacteria, and it increases by 50 bacteria every hour. How many bacteria
- 10. G: Given •Initial populationof bacteria: a1 = 100 •Increase in population per hour: d = 50 •Number of hours: n = 8 A: Asked How many bacteria will there be after 8 hours? : a8 = ? S: Solution an = a1 + ( n-1) d a8 = 100 + ( 8-1) 50 = 100 + (7) 50 = 100 + 350 After 8 hours, there will be 450 bacteria in the petri dish.
- 11.
- 12. Example Problem 1:Salary Increase
- 13. A recent graduatestarts a new job with starting salary of Php20,000.00. Each year, they receive a raise of Php 2,000.00. How much will their salary be in the 5th year?
- 14. G: Given •Starting salary:a1 = 20,000 •Increase in salary per year: d = 2,000 •Number of years: n = 5 A: Asked How much will their salary be in the 5th year? : a5 = ? S: Solution an = a1 + ( n-1) d a5 = 20,000 + ( 5-1) 50 = 20,000+(4) 2,000 = 20,000 + 8,000 The salary in the 5th year is Php 28,000.00
- 15. The first stepof a staircase is 10 cm high, and each step is 2 cm higher. What is the height of the 15th step?
- 16. “Generalize and Apply!" •What are the key learning points you took away from today's lesson? • How can arithmetic sequences be used to solve real-life problems? Can you give an example?
- 18. A plant grows4 cm each week. If it starts at 10 cm, how tall will it be after 8 weeks? G: Given A: Asked S: Solution
- 19. G: Given •Initial heightof the plant: a1 = 10 cm •Plant grows 4 cm each week: d = 4 cm •Number of weeks: n = 8 A: Asked How many bacteria will there be after 8 hours? : a8 = ? S: Solution an = a1 + ( n-1) d a8 = 10 + ( 8-1) 4 = 10 + (7) 4 = 10 + 28 The plant will be 38 cm tall after 8 weeks. 2 pts. 1 pt. 3 pts.
- 20. "Exit Tickets: Quick Insights forDeeper Understanding "
- 21. Exit Tickets • OneThing I Learned Today: •One Question I Still Have:
- 22. ASSIGNMENT . Solve thefollowing problems: . 1.Runner increases distance by 0.2 km each day, starting at 2 km. Find distance on day 10. . 2.Glenn bought a car Php600,000. The yearly depreciation of his car is 10% of its value at the start of the year. What is its value after 4 years?