Find the 8th term of the geometric sequence $$ 6,18,54, \ldots $$ Answer Attempt 1 out of 3

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To find the 8th term of the geometric sequence $$ 6, 18, 54, \ldots $$, we first need to identify the first term and the common ratio.

1. **Identify the first term ($$ a $$)**:
   The first term $$ a = 6 $$.

2. **Identify the common ratio ($$ r $$)**:
   The common ratio can be found by dividing the second term by the first term:
   $$
   r = \frac{18}{6} = 3
   $$

3. **Use the formula for the $$ n $$-th term of a geometric sequence**:
   The formula for the $$ n $$-th term of a geometric sequence is given by:
   $$
   a_n = a \cdot r^{n-1}
   $$
   where $$ a_n $$ is the $$ n $$-th term, $$ a $$ is the first term, $$ r $$ is the common ratio, and $$ n $$ is the term number.

4. **Calculate the 8th term ($$ a_8 $$)**:
   We will substitute $$ a = 6 $$, $$ r = 3 $$, and $$ n = 8 $$ into the formula:
   $$
   a_8 = 6 \cdot 3^{8-1} = 6 \cdot 3^7
   $$

5. **Calculate $$ 3^7 $$**:
   First, we calculate $$ 3^7 $$:
   $$
   3^7 = 2187
   $$

6. **Now calculate $$ a_8 $$**:
   $$
   a_8 = 6 \cdot 2187
   $$

Now, let's perform the multiplication to find $$ a_8 $$:
$$
a_8 = 6 \cdot 2187 = 13122
$$

Thus, the 8th term of the geometric sequence is $$ \boxed{13122} $$.
The 8th term of the geometric sequence is 13122.

Find the 8th term of the geometric sequence \( 6,18,54, \ldots \) Answer Attempt 1 out of 3

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