1. A tennis ball is dropped from a height of 100 cm. Each bounce reaches 80% of its previous height. What kind of sequence is formed by the heights?

2. Determine the missing letter in the sequence: M, L, N, O, K, J, P, Q, ___, H, R, S.

3. What is the next term in the sequence 2, 4, 8, 16, …?

4. Determine the next three terms of the sequence 5, 10, 20, 40, …

5. Find the first four terms of the sequence an = 3n − 1. 

6. The number of chairs in a hall doubles every year. If there were 50 chairs last year and 100 this year, what sequence describes this? 

7. The first term in an arithmetic sequence is 4 and the third term is 10. What is the second term? 

8. What is the 25th term of the sequence 2, 5, 8, 11, …? 

9. Anna saves ₱300 on the first week and increases her savings by ₱150 each week. How much will she save on the 10th week? 

10. What is the sum of the first 50 natural numbers? 

11. Is the sequence 1, 1.5, 2, 2.5, … arithmetic?    

12. What is the 12th term of the sequence 10, 15, 20, 25, …? 

13. Insert three arithmetic means between 12 and 28. 

14. Find the sum of the first 10 terms of the sequence 6, 4, 2, 0, … 

15. The 9th term of an arithmetic sequence is 35 and the first term is 5. What is the common difference? 

16. A staircase has 15 steps. The first step has 10 tiles, the second 12 tiles, the third 14 tiles, and so on. How many tiles are there in total? 

17. A company increases production from 500 to 650 phones over several weeks, adding 15 per week. How many weeks will it take to reach 650? 

18. If the sequence 40, 35, 30, 25, … has a difference of -5, what is the ratio of the geometric sequence 40, 20, 10, 5, …? 

19. For the series 3, 6, 12, 15, 30, 33, … find the rule and next term. 

20. The sequence 5, -10, 20, -40, … has a common ratio of:

21. An infinite geometric series has a sum if: 

22. Find the 6th term of the sequence 2, -6, 18, … 

23. Find the 8th term of 3, 9, 27, … 

24. A bacterial culture doubles daily. If there are 5 cells initially, how many on day 7? 

25. The 4th term of a geometric sequence is 81 and the first term is 3. Find r. 

26. In a geometric sequence starting at 2 with ratio 5, which term is 1250? 

27. What type of series is 64 + 32 + 16 + 8 + 4 + 2? 

28. Which has an infinite sum?

29. Find the sum of 1 + 3 + 9 + … + 729.

Find the geometric mean of 16 and 64.

Find three geometric means between 2 and 162.

32. In the harmonic sequence 1, 1/2, 1/3, … which term is 1/8?

33. The sum of an infinite geometric series is 48, and a₁ = 60. Find r.

34. Find the sum of the first 5 terms of 5, 10, 20, …

35. Find the 10th term of Fibonacci sequence 1, 1, 2, 3, …

36. Evaluate 1 − 1/2 + 1/4 − 1/8 + … to infinity.

37. A savings doubles daily starting at ₱5. How much is saved on day 8?

38. Find the sum of the first 6 terms of 3, 6, 12, …

39. Insert one geometric mean between 9 and 36.

40. Find the quotient when x³ + 2x² − 15x + 18 is divided by x − 3.

41. If x² + 1 is a factor of x⁴ − x² + 4x − 4, find the other factor.

42. In x² − 49 = (x − 7)(x + 7), the expressions (x − 7) and (x + 7) are called:

43. What is the quotient when 3x² − 12x + 9 is divided by x − 3?

44. Using long division to divide x³ − 4x² + 5x − 2 by x − 2, what operation produces the second line?

45. Factor x³ + 64 completely.

46. If P(x) = x³ − 4x² + 6x − 8 is divided by x − 2 using synthetic division, write the third row as a polynomial.

47. If (2x³ − 5x² + 4x − 1) is divided by (x − 1), what are the first-row numbers in synthetic division?

48. Which is a factor of x² − 16?

50. The perimeter of a rectangle is 40 cm and the area is 96 cm². If length is 4 cm longer than width, find the dimensions.