question\nfind the 10th term of the geometric sequence 3, 6, 12, ...

Explanation:

Step1: Find the common ratio

The common ratio $r$ of a geometric sequence is found by dividing a term by its previous term. For the sequence $3,6,12,\cdots$, $r=\frac{6}{3} = 2$.

Step2: Identify the first - term and the formula for the $n$th term

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 $a_1 = 3$, $r = 2$, and $n = 10$ into the formula $a_n=a_1r^{n - 1}$. So $a_{10}=3\times2^{10 - 1}=3\times2^9=3\times512 = 1536$.

Answer:

1536