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Four geometric means between 4 and 972 are
- a)12,30,100,324
- b)10, 8, 55, 89
- c)10,36,108,320
- d)12,36,108,320
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Four geometric means between 4 and 972 area)12,30,100,324b)10, 8, 55, ...
Let t1 = 4, t2, t3, t4, t5, t6 = 972 be the sequence.
Then; t6 = 972 ⇒ ar5 = 972 ⇒ 4r5 = 972
⇒ r5 = 243 = 35
⇒ r = 3
Hence the arithmetic means between 4 and 972 are 12, 36, 108, 324.
Then; t6 = 972 ⇒ ar5 = 972 ⇒ 4r5 = 972
⇒ r5 = 243 = 35
⇒ r = 3
Hence the arithmetic means between 4 and 972 are 12, 36, 108, 324.
Most Upvoted Answer
Four geometric means between 4 and 972 area)12,30,100,324b)10, 8, 55, ...
Finding the Geometric Mean
To find the geometric mean between two numbers, we take the square root of their product. To find multiple geometric means between two numbers, we repeat this process.
Option A: 12, 30, 100, 324
- √(12 x 30) = √360 ≈ 18.97
- √(18.97 x 100) ≈ 38.94
- √(38.94 x 324) ≈ 77.55
Option B: 12, 24, 108, 320
- √(12 x 24) = √288 ≈ 16.97
- √(16.97 x 108) ≈ 35.04
- √(35.04 x 320) ≈ 62.68
Option C: 10, 36, 108, 320
- √(10 x 36) = √360 ≈ 18.97
- √(18.97 x 108) ≈ 38.94
- √(38.94 x 320) ≈ 77.55
None of the options match the given numbers
None of the above options produce the given numbers of 4 and 972 as the starting and ending values, respectively. Therefore, the correct answer is option D, none of these.
To find the geometric mean between two numbers, we take the square root of their product. To find multiple geometric means between two numbers, we repeat this process.
Option A: 12, 30, 100, 324
- √(12 x 30) = √360 ≈ 18.97
- √(18.97 x 100) ≈ 38.94
- √(38.94 x 324) ≈ 77.55
Option B: 12, 24, 108, 320
- √(12 x 24) = √288 ≈ 16.97
- √(16.97 x 108) ≈ 35.04
- √(35.04 x 320) ≈ 62.68
Option C: 10, 36, 108, 320
- √(10 x 36) = √360 ≈ 18.97
- √(18.97 x 108) ≈ 38.94
- √(38.94 x 320) ≈ 77.55
None of the options match the given numbers
None of the above options produce the given numbers of 4 and 972 as the starting and ending values, respectively. Therefore, the correct answer is option D, none of these.
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