The third term of a G.P. is 12. The product of first five terms is _____.Choices:- 12^5 12^2 4^4 3^7

In a geometric progression (G.P.), the third term is given by a*r^2, where 'a' is the first term and 'r' is the common ratio.

Given that the third term is 12, we have a*r^2 = 12.

The product of the first five terms of a G.P. is given by (ar^4)(ar^3)(ar^2)(ar)(a) = a^5 * r^10.

We know that a*r^2 = 12, so we can substitute this into the equation for the product of the first five terms to get (12)^5 = 248832.

Therefore, the product of the first five terms is 248832. However, this option is not available in the choices given.

There seems to be a mistake in the question or the choices provided.

In a geometric progression (G.P.), the third term is given by a*r^2, where a is the first term and r is the common ratio. Given that the third term is 12, we have:

a*r^2 = 12

The product of the first five terms of a G.P. is given by (ar^0) * (ar^1) * (ar^2) * (ar^3) * (a*r^4), which simplifies to:

a^5 * r^10

Substituting a*r^2 = 12 into the equation for the product of the first five terms, we get:

(12/r^2)^5 * r^10 = 12^5 * r^0 = 12^5

So, the product of the first five terms is 12^5.