Question

find the 10th term of the geometric sequence 3, 15, 75, ... answer attempt 1 out of 2

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 and the formula

The first - term $a_1 = 3$, and the formula for the $n$th term of a geometric sequence is $a_n=a_1r^{n - 1}$.

Step3: Calculate the 10th term

Substitute $a_1 = 3$, $r = 5$, and $n = 10$ into the formula: $a_{10}=3\times5^{10 - 1}=3\times5^9$.
$5^9=1953125$, and $3\times1953125 = 5859375$.

Answer:

$5859375$