The given sequence is geometric, with the first term $a = 6$ and the common ratio $r = \frac{18}{6} = 3$.

The sum of the first $n$ terms of a geometric sequence is given by the formula:

$S_n = \frac{a(1 - r^n)}{1 - r}$

where:

• $S_n$ is the sum of the first $n$ terms,
• $a$ is the first term,
• $r$ is the common ratio,
• $n$ is the number of terms.

For the first four terms ($n = 4$):

$S_4 = \frac{6(1 - 3^4)}{1 - 3}$

Now let's calculate this:

$S_4 = \frac{6(1 - 81)}{1 - 3} = \frac{6(-80)}{-2} = \frac{-480}{-2} = 240$

Thus, the sum of the first four terms of the sequence is $S_4 = 240$.

Would you like more details on geometric sequences or have any questions?

---

Here are 5 related questions to explore:

1. How do you derive the formula for the sum of a geometric sequence?
2. What happens to the sum if the common ratio is less than 1?
3. Can you find the sum of the first 5 terms of this sequence?
4. What is the sum of an infinite geometric series if $|r| < 1$?
5. How does the common ratio affect the rate of growth of the sequence?

Tip: In a geometric sequence, if $|r| > 1$, the terms grow rapidly; if $|r| < 1$, the terms decrease toward zero.