Answer
The 5th term is $\frac{112}{81}$ The common ratio is $\frac{2}{3}$ $a_n = 7(\frac{2}{3})^{(n-1)}$
Work Step by Step
We are given the terms $7 \frac{14}{3} \frac{28}{9} \frac{56}{27}$. Since each term is multiplied by $\frac{2}{3}$ to get to the next term the common ratio is $\frac{2}{3}$. The 5th term is therefore the 4th term ($\frac{56}{27}$) $\times \frac{2}{3} = \frac{112}{81}$ To write a formula for the nth term of the geometric sequence start with the form $a_n = a(r)^{(n-1)}$ since a (the first term) = 7 and r (the common ratio) = $\frac{2}{3}$ the formula is $a_n = 7(\frac{2}{3})^{(n-1)}$
