nth term of a geometric sequence unique id: 3224\nscore: 0/6 penalty: none\nyou only have 6 questions left…

Explanation:

Step1: Identify the formula for the nth term of a geometric sequence

The formula for the nth term of a geometric sequence is $a_n = a_1 \times r^{(n - 1)}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.

Step2: Find the first term ($a_1$) and the common ratio ($r$)

For the sequence $3, 6, 12, \dots$:

• The first term $a_1 = 3$.
• The common ratio $r$ is found by dividing any term by its previous term. For example, $r = \frac{6}{3} = 2$ (or $\frac{12}{6} = 2$).

Step3: Substitute the values into the formula to find the 8th term

We need to find the 8th term, so $n = 8$. Substitute $a_1 = 3$, $r = 2$, and $n = 8$ into the formula: [ \begin{align*} a_8 &= 3 \times 2^{(8 - 1)} \ &= 3 \times 2^7 \ &= 3 \times 128 \ &= 384 \end{align*} ]

Answer:

384