Mechanical Engineering Review Online

1. The 3rd term of a harmonic progression is 30 and the 9th term is 12. Find the 11th term.

a. 9        

b. 10

c. 11

d. 12

2. What is the sum of the progression 4, 9, 14, 19… up to the 22nd term?

a. 1250

b. 1232

c. 1243

d. 1262

3. A rubber ball was dropped from a height of 30 m and each time it strikes the ground it rebounds to a height of 70% of the distance from which it fell. Find the total distance traveled by the ball before it comes to rest.

a. 165 m

b. 170 m

c. 175 m

d. 180 m

4. Find the 28th term of harmonic progression ½, ¼, 1/6, …

a. 1/50

b. 1/45

c. 1/56

d. 1/53

5. Find the sum of the infinite geometric series, 104, 52, 26,13, …

a. 208

b. 210

c. 212

d. 204

6. A truck loss power, and as it coasts it travels 22 feet in the first second, and each succeeding seconds it travels two-thirds as far as in the preceding second. How far does the truck travel until it completely stops?

a. 34 ft

b. 40 ft

c. 38 ft

d. 44 ft

7. Find the sum of the infinite geometric series with the first term of 10 and ratio of 0.5.

a. 16

b. 18

c. 22

d. 20

8. When dropped, a certain ball bounces back to 5/7 of its preceding height. If the ball is dropped from a window 25 feet above the ground, how far will the ball travel in its 6th bounce?

a. 3.64 ft

b. 4.56 ft

c. 5.36 ft

d. 6.64 ft

9. Find the sum of the first eight terms of the geometric series 5, 10, 20, …

a. 1260

b. 1275

c. 1284

d. 1290

10. If the 3rd term is 12 and 6th term is 96 are terms of a geometric progression, find the 15th term.

a. 49152

b. 49120

c. 49110

d. 49100

11. A geometric progression of 8 terms has last term 128 and the common ratio is 2. Find the first term.

a. 1

b. 2

c. 3

d. 4

12. Find the 14th term of the arithmetic progression 6, 1, -4, …

a. -55

b. -59

c. -62

d. -53

13. A ladder is to be constructed with 12 rungs that uniformly decrease in length. The bottom rung will be 30 inches long and the top of the rung will have a length of 18 inches. Find the board required for the 12 rungs.

a. 252 in

b. 280 in

c. 288 in

d. 285 in

14. Find the arithmetic mean between 12 and 4.

a. 5

b. 6

c. 7

d. 8

15. Find the common difference of the arithmetic progression for which the 3rd term is 8 and the 11th term is 80.

a. 9

b. 8

c. 7

d. 6

16. The geometric mean of 49 and 900 is ____.

a. 210

b. 220

c. 215

d. 200

17. In a pile of logs, each layer contains one more log than the layer above and the top contains just three logs. If there are 75 logs in the file, how many layers are there?

a. 12

b. 10

c. 14

d. 16

18. In an arithmetic progression the 5th term is 14 and the 8th term is 23. Find the 33rd term.

a. 96

b. 94

c. 98

d. 92

19. What is the sum of the following finite sequence of terms? 20, 27, 34, 41, …, 69.

a. 356

b. 350

c. 345

d. 366

20. Find x in the sequence 6, x, 22 so that the sequence will be arithmetic.

a. 9

b. 10

c. 11

d. 12

21. Find the sum of even numbers from 8 to 180.

a. 8120

b. 8210

c. 8178

d. 8173

22. The speed of an object falling from rest is directly proportional to the square root of the distance it has fallen. When it has fallen 30 ft, its speed is 45 ft/s. Find its speed when it has fallen 120 ft.

a. 85 fps

b. 88 fps

c. 83 fps

d. 90 fps

23. In a geometric sequence, the 9th term is 73/51 and r=3/2. Find the first term.

a. 0.0585

b. 0.0681

c. 0.0766

d. 0.0350

24. In a certain arithmetic sequence, the 25th term is 30 and the difference is 4. Find the first term.

a. -62

b. -66

c. -68

d. -64

25. The 6th term of an arithmetic progression is 22 and the 16th is 60. Find the common difference.

a. 21/5

b. 32/5

c. 19/5

d. 28/5

26. Find the 23rd term of the arithmetic sequence 2, 5, 8, 11, …

a. 68

b. 65

c. 62

d. 60

27. Find the ratio of an infinite geometric progression if the sum is 3 and the first tem is ¼.

a. 11/12

b. 13/12

c. 17/12

d. 12/11 

Answer Key (Handwritten)