Q 52. If the product of first 5 terms of gp is 243, find the middle term of a GP, I.e. the third term. Ops: A. 2 B. 4 C. 6 D. 3

The product of the first 5 terms of a geometric progression (GP) is given as 243.

Let's denote the first term of the GP as 'a' and the common ratio as 'r'.

The first 5 terms of the GP can be written as: a, ar, ar^2, ar^3, ar^4.

The product of these 5 terms is: a^5 * r^10 = 243.

We are asked to find the middle term of the GP, which is the third term, ar^2.

Since the product of the first 5 terms is 243, we can write the equation as: a^5 * r^10 = 243.

Taking the fifth root of both sides to isolate 'a', we get: a = (243)^(1/5) = 3.

Substituting 'a' back into the equation for the third term, we get: ar^2 = 3r^2.

Since we don't know the value of 'r', we can't find a specific numerical value for the third term. However, we know it will be some multiple of 3.

So, the closest answer from the options given is:

D. 3