**Geometric Progression (GP)**

Geometric Progression, also known as a geometric sequence, is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

The general form of a GP is:

a, ar, ar^2, ar^3, ...

where 'a' is the first term and 'r' is the common ratio.

**Given Information**

According to the given information, the second term of the GP is 24 and the fifth term is 81. Let's use this information to find the first term and the common ratio of the GP.

**Finding the First Term (a)**

The second term of the GP is 24, so we can write:

a * r = 24 ...(1)

**Finding the Fifth Term**

The fifth term of the GP is 81, so we can write:

a * r^4 = 81 ...(2)

**Solving Equations (1) and (2)**

To find the first term and the common ratio, we can solve equations (1) and (2) simultaneously.

Dividing equation (2) by equation (1), we get:

(a * r^4) / (a * r) = 81 / 24

Simplifying the equation, we have:

r^3 = 81 / 24

Calculating the right side of the equation, we get:

r^3 = 27 / 8

Taking the cube root of both sides, we find:

r = (27 / 8)^(1/3)

Calculating the value of r, we get:

r ≈ 1.5

Substituting the value of r in equation (1), we can solve for the first term 'a':

a * 1.5 = 24

a ≈ 16

**The Geometric Progression Series**

Now that we have found the first term (a ≈ 16) and the common ratio (r ≈ 1.5), we can write the GP series:

16, 24, 36, 54, 81, ...

**Explanation**

In this GP series, the first term is approximately 16, and each subsequent term is obtained by multiplying the previous term by 1.5. The second term is 24, which is obtained by multiplying the first term (16) by the common ratio (1.5). Similarly, the fifth term is 81, which is obtained by multiplying the fourth term (54) by the common ratio (1.5).

The series starts with the first term 16 and continues with each term being 1.5 times the previous term. The series follows a pattern where each term is multiplied by the common ratio to obtain the next term.

The given information allows us to determine the values of the first term and the common ratio, which in turn helps us generate the GP series.