Problem Solving in Arithmetic sequence.pptx

Solving Problem in Arithmetic Sequence

1. What’s new! Suppose you participate 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 Participants (n) Total Amount Raised 1 5 2 2 50 3 450 … … 75 14,850 a n = a 1 + ( n-1) d a 75 = 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: Initial donation: Php 50.00 Each participant raises: Php 200.00 Number of participants: 75 a 1 = 50 n= 75 d= 200 Therefore, the minimum amount of money raised with 75 participants is Php 14, 850.00.

3. "Where Else Do We See Arithmetic Sequences in Daily Life?"

4. Solving Real-Life Problems Involving Arithmetic Sequences

5. solve real-life problems involving arithmetic sequences by applying the formula for the nth term; 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.

6. G iven a 1 n d "GAS Up Your Problem-Solving!" A sked a n=? S olution a n = a 1 + ( n-1) d

7. Example Problem: Bacterial Growth In a 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 in biological research.

8. A scientist is observing 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 will there be after 8 hours?

9. G: Given Initial population of bacteria: a 1 = 100 Increase in population per hour: d = 50 Number of hours: n = 8 A: Asked How many bacteria will there be after 8 hours? : a 8 = ? S: Solution a n = a 1 + ( n-1) d a 8 = 100 + ( 8-1) 50 = 100 + (7) 50 = 100 + 350 = 450 After 8 hours, there will be 450 bacteria in the petri dish.

10. “Mastering the Basics: Your Guided Practice”

11. Example Problem 1: Salary Increase

12. A recent graduate starts 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 5 th year?

13. G: Given Starting salary: a 1 = 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? : a 5 = ? S: Solution a n = a 1 + ( n-1) d a 5 = 20,000 + ( 5-1) 50 = 20,000+(4) 2,000 = 20,000 + 8,000 = 28, 000 The salary in the 5 th year is Php 28,000.00

14. The first step of a staircase is 10 cm high, and each step is 2 cm higher. What is the height of the 15 th step?

15. “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?

16. A plant grows 4 cm each week. If it starts at 10 cm, how tall will it be after 8 weeks? G: Given A: Asked S: Solution

17. G: Given Initial height of the plant: a 1 = 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? : a 8 = ? S: Solution a n = a 1 + ( n-1) d a 8 = 10 + ( 8-1) 4 = 10 + (7) 4 = 10 + 28 = 38 cm The plant will be 38 cm tall after 8 weeks. 2 pts. 1 pt. 3 pts.

18. " Exit Tickets : Quick Insights for Deeper Understanding"

19. Exit Tickets One Thing I Learned Today: One Question I Still Have:

20. ASSIGNMENT Solve the following 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?