Question

exponents and exponential functions
finding a specified term of a geometric sequence give...
find the $12^{\text{th}}$ term of the following geometric sequence.
$2, 6, 18, 54, \dots$

Explanation:

Step1: Identify $a_1$ and $r$

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

Step2: Use the geometric sequence formula

The formula for the $n$th term of a geometric sequence is $a_n = a_1 \cdot r^{n - 1}$. For the 12th term, $n = 12$, $a_1 = 2$, $r = 3$. Substitute these values: $a_{12}=2\cdot3^{12 - 1}=2\cdot3^{11}$.

Step3: Calculate $3^{11}$ and multiply by 2

First, $3^{11}=177147$. Then, $2\times177147 = 354294$.

Answer:

354294