Answer
The fourth term = $\frac{24}{25}$
Work Step by Step
1. Find the common ratio. The 2nd term (6) is the first term (15) multiplied by $\frac{2}{5}$ so the common ratio, r, = $\frac{2}{5}$
2. Find the first term: The first term is given as 15. The first term = a.
3. Create a formula for the geometric sequence in the form $a_{n} = a(r)^{n-1}$ : $a_n = 15(\frac{2}{5})^{n-1}$
4. Plug in n = 4 to get the fourth term: $a_n = 15(\frac{2}{5})^{4-1}$ = $15(\frac{2}{5})^{3}$ =$ \frac{24}{25}$
