Insertion of arithmetic and geometric means - One Line Questions

1. Insert 2 arithmetic means between -5 and 13. — -1, 7
2. Insert 4 geometric means between 1/2 and 128. — 2, 4, 8, 16
3. If 4 numbers are in geometric progression, their product is 256. If 2, 6, 8, and 50 are added to them respectively, the new numbers are in arithmetic progression. Find the numbers. — 2, 4, 8, 16
4. Insert 4 geometric means between 1/2 and 16. — 1/2, 1, 2, 4
5. Insert 4 geometric means between 1/3 and 243. — 1, 3, 9, 27
6. Insert 3 geometric means between 1/4 and 16. — 1/2, 1, 2
7. Insert 3 geometric means between 1/8 and 128. — 1/2, 2, 8
8. Insert 2 geometric means between 1/2 and 1/16. — 1/4, 1/8
9. Insert 2 geometric means between 1/4 and 1/64. — 1/8, 1/16
10. Insert 3 geometric means between 1/27 and 27. — 1/9, 1, 9
11. If 3 numbers are in arithmetic progression, their sum is 45. If 1, 4, and 19 are added to them respectively, the new numbers are in geometric progression. Find the numbers. — 10, 15, 20
12. Insert 2 arithmetic means between 7 and 25. — 13, 19
13. Insert 3 arithmetic means between 10 and 26. — 14, 18, 22
14. Insert 2 arithmetic means between 10 and 30. — 15, 20
15. Insert 5 arithmetic means between 10 and 40. — 15, 20, 25, 30, 35
16. Insert 2 geometric means between 5 and 45. — 5 * sqrt(3), 15 * sqrt(3)
17. If a, b, c are in geometric progression, then a/(b+a) + c/(b+c) is equal to: — 2
18. The arithmetic mean of two numbers is 6 and their geometric mean is 4. Find the numbers. — 2, 10
19. The product of three numbers in geometric progression is 1000. If 6 and 8 are added to the first and second numbers respectively, then the new numbers are in arithmetic progression. Find the numbers. — 2, 10, 50
20. Insert 4 arithmetic means between -2 and 18. — 2, 6, 10, 14
21. If the arithmetic mean of two positive numbers is twice their geometric mean, then the numbers are in the ratio. — 4:1
22. If the geometric mean of two numbers is 6 and their arithmetic mean is 7.5, find the numbers. — 3, 12
23. The arithmetic mean of two numbers is 15 and their geometric mean is 9. Find the numbers. — 3, 27
24. The sum of three numbers in arithmetic progression is 21 and their product is 231. Find the numbers. — 3, 7, 11
25. If the sum of three numbers in geometric progression is 21 and their product is 729, find the numbers. — 3, 9, 27
26. The sum of three numbers in geometric progression is 39, and their product is 729. Find the numbers. — 3, 9, 27
27. If the arithmetic mean of two numbers is 10 and their geometric mean is 8, find the numbers. — 4, 16
28. The geometric mean of two numbers is 8. If 6 is added to the first number and 4 is added to the second number, the resulting numbers are equal. Find the numbers. — 4, 16
29. Insert 3 geometric means between 8 and 1/27. — 8/3, 8/9, 8/27
30. Insert 3 arithmetic means between 1 and 17. — 4, 7, 10
31. Insert 4 arithmetic means between 1 and 16. — 4, 7, 10, 13
32. Insert 5 geometric means between 2 and 128. — 4, 8, 16, 32, 64
33. Insert 5 arithmetic means between 2 and 20. — 5, 8, 11, 14, 17
34. Insert 3 geometric means between 3 and 48. — 6, 12, 24
35. Insert 4 geometric means between 3 and 96. — 6, 12, 24, 48
36. Insert 3 geometric means between 2 and 162. — 6, 18, 54
37. The sum of two numbers is 12 and their geometric mean is 6. Find the numbers. — 6, 6
38. Insert 2 arithmetic means between 4 and 16. — 8, 12
39. Insert 4 arithmetic means between 5 and 25. — 9, 13, 17, 21
40. If the arithmetic mean of two numbers is A and their geometric mean is G, find the numbers. — A + sqrt(A^2 - G^2), A - sqrt(A^2 - G^2)
41. If a, b, c are in arithmetic progression and a, b, c are also in geometric progression, then: — a = b = c
42. If a, b, c are in geometric progression, then (a+b+c)(a-b+c) is equal to: — a^2 + b^2 + c^2
43. If a, b, c are in arithmetic progression and a, b, c are in geometric progression, then which statement is true? — a=b=c
44. If a, b, c are in geometric progression, then log(a^x), log(b^x), log(c^x) are in: — Arithmetic progression
45. If a, b, c are in geometric progression, then log(a), log(b), log(c) are in: — Arithmetic progression
46. If a, b, c are in arithmetic progression and b, c, d are in geometric progression, then a, c, d^2 are in: — Geometric progression
47. If a, b, c are in geometric progression, then which of the following is true? — b^2 = ac
48. If a, b, c are in arithmetic progression, then which of the following is true? — b = (a+c)/2
49. If a, b, c are in arithmetic progression and b, c, d are in geometric progression, then which of the following is true? — c^2 = bd
50. If a, b, c are in geometric progression, then log a, log b, log c are in: — Arithmetic progression
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