5 sentences makes Geometric progression. their multiplying is 243.

how much is the multiplying first sentence and fifth sentence?

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- Oct 16th 2013, 10:46 AMparmisGeometric progression
5 sentences makes Geometric progression. their multiplying is 243.

how much is the multiplying first sentence and fifth sentence? - Oct 16th 2013, 11:16 AMebainesRe: 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$\displaystyle a \times ar \times ar^2 \times ar^3 \times ar^4= a^5r^{10}$ . The product of the 1st and 5th terms is $\displaystyle a^2r^4$, which is equal to $\displaystyle (a^5r^{10})^{2/5}$. Hence the product of the 1st and 5th terms is $\displaystyle 243^{2/5}$. Since $\displaystyle 243 = 3^5$, this becomes $\displaystyle (3^5)^{2/5} = 3^2=9$.