✅Task: Creating a Compilation of Problems with Solutions ✅List of Lessons:
Lesson 1. Arithmetic Sequence Lesson
2. Arithmetic Mean Lesson
3. Sum of Arithmetic Sequence Lesson
4. Geometric Sequence Lesson
5. Geometric Mean Lesson
6. Sum of Geometric Sequence
✅Each problem should have complete solution. Follow this format
Given:
Formula:
Solution:
Conclusion/Final Answer:
✅Each problem should be unique. ✅Ensure that the problems are clear, concise, and free from errors.
✅Write the Problems in bondpaper, handwritten/printed.
✅The Solution should be in handwritten.
Take note: Real-life Problems po dapat, hindi lang basta "find the arithmetic sequence of 1, 2, 3, ..."
Sample: Twelve days before Valentine’s Day, Carl decided to give Nicole flowers according to the Fibonacci sequence. On the first day, he sent one red rose, on the second day, two red roses, and so on. How many roses did Nicole receive during the tenth day?
and ang conclusion or final answer ay yung may
Therefore, Nicole will receive ...
gawin pong sentence ang conclusion.
again, 1 problem each lesson sa bondpaper ilalagay.
Lesson 1. Arithmetic Sequence Lesson
2. Arithmetic Mean Lesson
3. Sum of Arithmetic Sequence Lesson
4. Geometric Sequence Lesson
5. Geometric Mean Lesson
6. Sum of Geometric Sequence
✅Each problem should have complete solution. Follow this format
Given:
Formula:
Solution:
Conclusion/Final Answer:
✅Each problem should be unique. ✅Ensure that the problems are clear, concise, and free from errors.
✅Write the Problems in bondpaper, handwritten/printed.
✅The Solution should be in handwritten.
Take note: Real-life Problems po dapat, hindi lang basta "find the arithmetic sequence of 1, 2, 3, ..."
Sample: Twelve days before Valentine’s Day, Carl decided to give Nicole flowers according to the Fibonacci sequence. On the first day, he sent one red rose, on the second day, two red roses, and so on. How many roses did Nicole receive during the tenth day?
and ang conclusion or final answer ay yung may
Therefore, Nicole will receive ...
gawin pong sentence ang conclusion.
again, 1 problem each lesson sa bondpaper ilalagay.
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Lesson 1: Arithmetic Sequence
Given: A bus leaves a station every 20 minutes. The first bus leaves at 6:00 am.
Question: What time does the 5th bus leave?
Formula: An = A1 + (n-1)d
Solution: To find the time the 5th bus leaves, plug in the values into the formula: A5 = 6:00 + (5-1)*20 minutes = 6:00 + 80 minutes = 7:20 am.
Conclusion/Final Answer: Therefore, the fifth bus leaves at 7:20 am.
Lesson 2: Arithmetic Mean
Given: A runner's times for a 5km race over 4 races were 25, 27, 26, and 28 minutes.
Question: What was the runner's average time?
Formula: Arithmetic Mean = Sum of terms / Number of terms
Solution: Arithmetic Mean = (25 + 27 + 26 + 28) / 4 = 106 / 4 = 26.5 minutes.
Conclusion/Final Answer: Therefore, the runner's average time for the 5km race was 26.5 minutes.
Lesson 3: Sum of Arithmetic Sequence
Given: A worker saves $100 in the first month, and each month after that he saves $20 more than the previous month.
Question: How much money will the worker have saved after 6 months?
Formula: Sum = n/2 * (2A1 + (n-1)d)
Solution: Sum = 6/2 * (2*100 + (6-1)*20) = 3 * (200 + 100) = 3 * 300 = $900.
Conclusion/Final Answer: Therefore, the worker will have saved $900 after 6 months.
Lesson 4: Geometric Sequence
Given: A bacteria population doubles every hour.
Question: How many bacteria will there be after 5 hours if the initial population was 500?
Formula: An = A1 * r^(n-1)
Solution: A5 = 500 * 2^(5-1) = 500 * 16 = 8000.
Conclusion/Final Answer: Therefore, there will be 8000 bacteria after 5 hours.
Lesson 5: Geometric Mean
Given: In a certain investment, the value doubles every year.
Question: If the initial investment was $100, what would be the average value of the investment over the first 3 years?
Formula: Geometric Mean = (A1 * An)^(1/n)
Solution: Geometric Mean = (100 * 400)^(1/3) = 200^(1/3) = $5.85 (approx).
Conclusion/Final Answer: Therefore, the average value of the investment over the first 3 years would be approximately $5.85.
Lesson 6: Sum of Geometric Sequence
Given: A car's value depreciates by 20% each year. The car was originally worth $20,000.
Question: What is the total value of the car over 3 years?
Formula: Sum = A1 * (1 - r^n) / (1 - r) if r ≠ 1
Solution: Sum = 20000 * (1 - (0.8)^3) / (1 - 0.8) = 20000 * 0.488 / 0.2 = $48,800.
Conclusion/Final Answer: Therefore, the total value of the car over 3 years would be $48,800.