Question

There are n arithmetic means between 9 and 27. If the ratio of the last mean to the first mean is 2:1, find the value of n.

Answer 1

Given: there are n arithmetic means between 9 and 27

To find: if the ratio of the last mean to the first mean is 2 : 1, then find the value of n

Solution:

• Let the common difference be d
• Then the first mean is 9 + d
• and the last mean is 27 - d

By the given condition,

• 27 - d : 9 + d = 2 : 1
• or, (27 - d) / (9 + d) = 2 / 1
• or, 27 - d = 2 (9 + d)
• or, 27 - d = 18 + 2d
• or, 2d + d = 27 - 18
• or, 3d = 9
• or, d = 9 / 3
• or, d = 3

Let progression of the arithmetic means is

12, 15, 18, 21, 24.

Thus n = 5

Answer: the value of n is 5.

Answer 2

Answer:

5 is a correct answer

Step-by-step explanation:

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