Geometric progression

I think what you mean is this:

Given that a geometric series of 5 terms multiplies to 243, what is the product of the first and fifth term?

The product of 5 terms of a geometric series is $a \times ar \times ar^2 \times ar^3 \times ar^4= a^5r^{10}$ . The product of the 1st and 5th terms is $a^2r^4$ , which is equal to $(a^5r^{10})^{2/5}$ . Hence the product of the 1st and 5th terms is $243^{2/5}$ . Since $243 = 3^5$ , this becomes $(3^5)^{2/5} = 3^2=9$ .