Math Help - Geometric progression

1. Geometric progression

5 sentences makes Geometric progression. their multiplying is 243.
how much is the multiplying first sentence and fifth sentence?

2. Re: 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 $(3^5)^{2/5} = 3^2=9$.