question\nfind the 10th term of the geometric sequence 3, 15, 75, ...

Explanation:

Step1: Find the common ratio

The common ratio $r$ of a geometric sequence is found by dividing a term by its previous term. So $r=\frac{15}{3}=5$.

Step2: Identify the first - term

The first - term $a_1 = 3$.

Step3: Use the formula for the $n$th term of a geometric sequence

The formula for the $n$th term of a geometric sequence is $a_n=a_1r^{n - 1}$. Here, $n = 10$, $a_1=3$, and $r = 5$. So $a_{10}=3\times5^{10 - 1}$.

Step4: Calculate the value

$a_{10}=3\times5^{9}=3\times1953125 = 5859375$.

Answer:

$5859375$