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Find the harmonic mean between the numbers 3/8 and 4. a. 35/34 c. 42/35 b. 24/35 d. 35/24 Find the sum of the first 12 terms of an arithmetic progression whose 7 th term is 5/3 and with a common difference of -2/3. a. 22 c. 26 b. 24 d. 28 How many arithmetic means must be inserted between 1 and 36 so that the sum of the resulting arithmetic progression will be 148? a. 5 b. 6 c. 7 d. 8 How many terms of the arithmetic progression 9,11,13,.. must be added in order that the sum should be equal the sum of the first nine terms of the geometric progression 3,-6,12,- 24,…? a. 18 b. 19 c. 20 d. 21 How many arithmetic means must be inserted between 1 and 36 so that the sum of all numbers in the resulting progression will be 148? a. 4 b. 3 c. 5 d. 6 The positive value of x so that x, x 2-5 and 2x will be in harmonic progression is a. 6 b. 5 c. 4 d. 3 The 3 rd term of a harmonic progression is 15 and the 9 th term is 6. Find the 11 th term. a. 4 b. 8 c. 5 d. 7 Find x so that x-1, x+2, and x+8 are the first three terms of a geometric progression. a. 4 b. 3 c. 5 d. 2
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What must be the value of x in the arithmetic progression x-7, x-2, x- 2, x+3, … so that its 10 th term will be 40? a. 4 b. 3 c. 2 d. 1
10. The 3rd term of an arithmetic progression is 4 and the 9 th term is -14. Find the sum of the first six terms. a. 21 b. 19 c. 17 d. 15 11. How many consecutive numbers beginning with5 must be taken for their sum to be equal to 95? a. 12 b. 11 c. 10 d. 9 12. The ratio of three numbers is 2:5:7. If 7 is subtracted from the second number, the resulting number form an arithmetic progression. Determine the smallest of the three numbers. a. 28 b. 15 c. 21 d. 70 13. Find the 50 th term of 1+i, 2+4i, 3+7i, … a. 47 + 148i b. 48 + 148i c. 49 + 148i d. 50 + 148i 14. Find the 10 th term in an arithmetic progression where the first term is 3 and whose 1 st, 4th and 13th terms form a geometric progression. a. 21 b. 22 c. 23 d. 24 15. The sum of the first three terms of an arithmetic progression is-3 while the sum of the first five terms of the same arithmetic progression is 10. Find the first term. a. -5 b. -4 c. -3 d. -2
16. If the first term and third term of a harmonic progression are 5/21 and 5/23 respectively, find the 6 th term a. 26/5 b. 27/5 c. 24/5 d. 23/5 17. How many consecutive terms must be taken form the sequence 3, -6, -12, - 24, … for the sum to equal 8193? a. 11 b. 12 c. 13 d. 14 18. Find the 8 th term of 5 x+1, 52x+1, 53x+1, …. a. 56x+1 b. 57x+1 c. 58x+1 d. 59x+1 19. Find the common ratio of a geometric progression whose first term is 1 and for which the sum of the first 6 terms is 28 times the sum of the first 3 terms. a. 2 b. 3 c. 4 d. 5 20. Find the sum of all positive integers between 84 and 719 which are exactly divisible by 5. a. 23750 b. 45680 c. 50800 d. 38460 21. In a certain A.P, the 1 st, 4th and 8th terms are themselves form a geometric progression. What is the common ratio of the G.P? a. 4/3 b. 5/4 c. 4/5 d. ¾ 22. The 1 st term of an arithmetic progression is 6 and the 10 th term is 3 times the 2 nd term. What is the common difference? a. 1 b. 2 c. 3 d. 4 23. The 3rd term of a geometric progression is 5 and the 6 th term is -40. Find the 8 th term. a. -140 b. -150 c. -160 d. -170
24. The 4 th term of a geometric progression is 343 and the 6 th term is 16807. Find the 8 th term. a. 853,243 b. 835,432 c. 824,533 d. 823,543 25. The arithmetic mean of the two positive numbers exceeds their geometric mean by 2. Find the smalle number if it is 40 less than the larger number. a. 90 b. 101 c. 121 d. 81 26. Find the sum of the first five terms of the geometric progression if the 3 rd term is 144 and 6th term is 486. a. 844 b. 972 c. 746 d. 548 27. How many terms of the progression 4, 7, 10, 13, …. Must be taken so that the sum will be 69. a. 6 b. 9 c. 8 d. 12 28. A ball is dropped from a height of 28cm. If it is always rebounds ½ of the height from which it falls, how far does it travel after the fifth bounce? 80.5 cm a. 372 cm b. 374 cm c. 376 cm d. 378 cm 29. If 1 + x + x 2 + … = ¼, find the value of x. a. -1/2 b. -1/3 c. -1/4 d. -1/5 30. Find the sum of the infinity of 1 – ½ + ¼ - 1/8 + … a. 1/3 b. 2/3 c. ¼ d. ¾ 31. The bob of a pendulum swings through an arc of 24cm long on its first swing. If each successive swing is approximately 5/6 the length of the preceeding swing, find the approximate total distance it travels before coming to rest. a. 121 cm b. 114 cm c. 144 cm d. 169 cm
32. Solve for x in the equation x + 3x + 5x + 7x + … + 49x = 625. a. ¼ b. ½ c. 1 d. 2 33. Find the sum of all integers between 90 and 190 if each integer is exactly divisible by 17? a. 847 b. 857 c. 867 d. 887 34. If 1/a, 1/b and 1/c are consecutive terms of an arithmetic progression, then b equals a. 2ac/(a+c) b. ac/(a+c) c. (a+c)/2ac d. (a+c)/ac 35. For a geometric progression for which the first term is x+y and the common ratio is the reciprocal of the first term, find the 10 th term. a. (x+y)-5 b. (x+y)-6 c. (x+y)-7 d. (x+y)-8
36. The first term of a geometric progression is 3 and the last term is 48. If each term is twice the previous term, find the sum of the geometric progression. a. 93 b. 92 c. 91 d. 90 37. A woman started a chain letter by writing to four friends and requesting each to copy a letter and send it to four other friends. If the chain was unbroken until the 5 th set of letters was mailed, how much spent for postage at P8.00 per letter? a. 16,219 b. 10,912 c. 21,835 d. 13,291 38. A soccer ball is dropped from a height of 6m. On each rebound it rises 2/3 of the height form which it last fell. What distance has it travelled at the instant it strikes the ground for the 7 th time? a. 27.89 m b. 19.86 m c. 20.87 m d. 24.27 m
39. If the sum is 220 and the first term is 10, find the common difference if the last term is 30. a. 2 b. 5 c. 3 d. 2/3 40. In the arithmetic progression -9, - 2, 5, … which term is 131? a. 20 b. 21 c. 22 d. 23 41. In a geometric progression, if the first term is x 2 and the common ratio is x 4, which term is x 18? a. 4th b. 5th c. 6th d. 7th 42. The arithmetic mean of two numbers is 4 and their harmonic mean is 15/4. Find the numbers. a. 3 and 5 b. 1 and 7 c. 2 and 6 d. 0 and 8 43. What value of x makes the three terms x, x/(x+1) and 3x/[(x+1)(x+2)] those of a geometric sequence? a. 1 b. ½ c. ¼ d. -1/2
44. Find the ratio of the infinite geometric series if the sum is 2 and the first term is ½. a. 1/3 b. 1/2 c. 3/4 d. 1/4 45. Determine the 7 th term of the arithmetic progression 3xy – y, 2xy, xy + y, … a. 5y – 3xy b. 5y + 3xy c. 5x – xy d. 5x + xy 46. If a, b, 2b - a, …. Is an arithmetic progression, find the next term. a. 2b – 3a b. 3b – 2a c. 2b + 3a d. 2b + a
47. A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer and sol until there are 10 bricks in the last layer. How many bricks are thre together? a. 638 b. 637 c. 640 d. 639 48. If x, y and 5x are three consecutive terms of an arithmetic progression whose sum is 81, find x. a. 9 b. 10 c. 11 d. 12 49. Once a month a man put some money into the cookie jar. Each month he put 50 cents more into the jar than the month before. After 12 years he counted his money, he had P5436. How much did he put in the jar in the last month? a. P73.50 b. P75.50 c. P74.50 d. P72.50 50. The seventh term is 56 and the 12 th terms is 1792 of the geometric progression. Find the ratio and the first term. Assume the ratios are equal. a. -2, 7/8 b. -1, 5/8 c. -1, 7/8 d. -2, 5/8
