Answer:
The explicit rule for a geometric sequence is given by the formula:
\(a_n = a_1 \cdot r^{(n-1)}\)
where:
- \(a_n\) is the \(n\)th term of the sequence,
- \(a_1\) is the first term of the sequence,
- \(r\) is the common ratio of the sequence,
- \(n\) is the position of the term in the sequence.
In this formula, each term of the sequence is obtained by multiplying the previous term by the common ratio (\(r\)). The first term (\(a_1\)) serves as the starting point of the sequence. The exponent \((n-1)\) indicates the position of the term in the sequence, where the first term is at position 1.
It allows us to find any specific term in a geometric sequence by plugging in the values of the first term (\(a_1\)), the common ratio (\(r\)), and the position of the term (\(n\)) into the formula.