**Given Information:**

- A1 and A2 are two arithmetic means between 1/3 and 1/24.

**To Find:**

The values of A1 and A2.

**Solution:**

Let's first find the common difference (d) of the arithmetic sequence.

The first term of the sequence is 1/3, and the second term is 1/24.

The common difference (d) can be found by subtracting the first term from the second term:

d = 1/24 - 1/3

To subtract fractions, we need a common denominator. The least common denominator of 24 and 3 is 24.

d = (1/24) - (8/24)

d = -7/24

Now that we have the common difference (d), we can find the values of A1 and A2.

**Finding the Value of A1:**

A1 is the arithmetic mean between 1/3 and 1/24. It is located one term after the first term (1/3) in the arithmetic sequence.

To find A1, we add the common difference (d) to the first term (1/3):

A1 = (1/3) + (-7/24)

To add fractions, we need a common denominator. The least common denominator of 3 and 24 is 72.

A1 = (1/3)(24/24) + (-7/24)(3/3)

A1 = 24/72 - 21/72

A1 = 3/72

A1 = 1/24

**Finding the Value of A2:**

A2 is the arithmetic mean between 1/3 and 1/24. It is located two terms after the first term (1/3) in the arithmetic sequence.

To find A2, we add twice the common difference (2d) to the first term (1/3):

A2 = (1/3) + 2(-7/24)

A2 = (1/3) - (14/24)

A2 = (1/3)(8/8) - (14/24)(1/1)

A2 = 8/24 - 14/24

A2 = -6/24

A2 = -1/4

**Final Answer:**

The values of A1 and A2 are:

A1 = 1/24

A2 = -1/4

Therefore, the correct answer is:

d) 1/24, -1/4

1/3, A1, A2 , 1/24 are in AP

Let A1 = 1/3+d
A2 = 1/3+2d

So 1/24 = 1/3+ 3d

solving it we get d= -7/72

so A1= 17/72
A2 = 10/72 = 5/36