Question

Insert 5 arithmetic means between a and 30 such that the 4th mean is 24. Also, find a.

If 5 arithmetic means are inserted between a and 30, and the 4th mean is 24, what is the value of 'a'?

A) 6

B) 12

C) 18

D) 20

Answer 1

To find the value of 'a', we need to determine the common difference of the arithmetic progression. Since the 4th mean is 24, and there are 5 arithmetic means between 'a' and 30, we can calculate the common difference as follows: 24 = a + 3d (1st mean = 'a' + d).

Step-by-step explanation:

To find the value of 'a', we need to determine the common difference of the arithmetic progression. Since the 4th mean is 24, and there are 5 arithmetic means between 'a' and 30, we can calculate the common difference as follows:

24 = a + 3d (1st mean = 'a' + d)

30 = a + 8d (6th mean = 'a' + 5d)

Subtracting equation (1) from equation (2) gives:

6 = 5d ⇒ d = 6/5 = 1.2

Substituting the value of d into equation (1) gives:

24 = a + 3(1.2) ⇒ a = 24 - 3.6 = 20.4

Therefore, the value of 'a' is approximately 20.4.