To find the equation that describes the given sequence \(8, 24, 72, \ldots\), we can begin by examining the pattern in the sequence.
- Identify the ratio between terms:
- \( \frac{24}{8} = 3 \)
- \( \frac{72}{24} = 3 \)
This indicates that each term is multiplied by 3 to get the next term.
- Express the terms:
- The first term \(a_1 = 8\)
- The second term \(a_2 = 8 \times 3 = 24\)
- The third term \(a_3 = 8 \times 3^2 = 72\)
Since each term can be expressed as an initial term multiplied by \(3\) raised to a power, we can express the \(n\)-th term of the sequence as follows:
\[ a_n = 8 \times 3^{n-1} \]
Thus, the equation for the \(n\)-th term in the sequence is:
\[ a_n = 8 \times 3^{n-1} \]
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