Question

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

Explanation:

Step1: Identify common ratio $r$

$r = \frac{6}{3} = 2$

Step2: Recall geometric term formula

The $n$-th term of a geometric sequence is $a_n = a_1 r^{n-1}$, where $a_1=3$, $n=10$, $r=2$.

Step3: Substitute values into formula

$a_{10} = 3 \times 2^{10-1} = 3 \times 2^9$

Step4: Calculate the power and product

$2^9 = 512$, so $a_{10} = 3 \times 512$

Answer:

1536