Question

find the 8th term of the geometric sequence 3, 6, 12, ...

Explanation:

Step1: Identify $a_1$ and $r$

In a geometric sequence, the first term $a_1 = 3$. The common ratio $r$ is found by dividing the second term by the first term: $r=\frac{6}{3}=2$.

Step2: Use the geometric sequence formula

The formula for the $n$th term of a geometric sequence is $a_n = a_1 \cdot r^{n - 1}$. We need to find the 8th term, so $n = 8$. Substitute $a_1 = 3$, $r = 2$, and $n = 8$ into the formula: $a_8=3\times2^{8 - 1}$.

Step3: Calculate the exponent and the result

First, simplify the exponent: $8 - 1 = 7$. Then calculate $2^7 = 128$. Now multiply by 3: $3\times128 = 384$.

Answer:

384