1. The problem is to understand the concept of a geometric sequence. 2. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio $r$. 3. The general formula for the $n$-th term of a geometric sequence is: $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 4. Important rules: - If $|r| > 1$, the terms grow in magnitude. - If $|r| < 1$, the terms get smaller and approach zero. - If $r$ is negative, the terms alternate in sign. 5. Example: If the first term $a_1 = 3$ and the common ratio $r = 2$, then the sequence is $3, 6, 12, 24, ...$ 6. To find the 5th term: $$a_5 = 3 \times 2^{5-1} = 3 \times 2^4 = 3 \times 16 = 48$$ 7. This means the 5th term in this geometric sequence is 48. This explanation covers the basics of geometric sequences and how to find any term using the formula.