The given problem is in the context of a geometric sequence, where:

• $a_2 = 6$ is the second term of the sequence.
• $r = 3$ is the common ratio.

We need to find the first term, $a_1$, to proceed with the calculation of further terms if necessary. In a geometric sequence, the $n$-th term is given by:

$a_n = a_1 \cdot r^{n-1}$

For $n = 2$: $a_2 = a_1 \cdot r^{2-1} = a_1 \cdot r$

Substitute the known values: $6 = a_1 \cdot 3$

Now, solve for $a_1$: $a_1 = \frac{6}{3} = 2$

Thus, the first term $a_1 = 2$.

If you need to find additional terms or have further questions, please let me know!

Related Questions

1. How do you find the third term $a_3$ in this sequence?
2. What is the formula to find any term $a_n$ in a geometric sequence?
3. How can we find the sum of the first $n$ terms in a geometric sequence?
4. How does changing the common ratio affect the sequence?
5. Can we determine the type of sequence by only looking at the terms?

Tip

Always start by identifying if the problem involves an arithmetic or geometric sequence, as this will determine the approach and formulas to use.