To describe the given sequence \(-5, -10, -20, \ldots\), we can observe that each term can be derived from the previous term by multiplication by 2 and the first term is \(-5\).
To find a formula for the \(n\)-th term \(a_n\):
- Identify the pattern:
- The first term \(a_1 = -5\)
- The second term \(a_2 = -10 = -5 \times 2\)
- The third term \(a_3 = -20 = -10 \times 2\)
The relationship between the terms suggests that each term can be expressed as a multiple of \(-5\).
- Determine the general formula: The \(n\)-th term can be expressed as: \[ a_n = -5 \times 2^{(n-1)} \]
Thus, the equation for the sequence in terms of \(n\), where \(n=1\) for the first term, is:
\[ a_n = -5 \cdot 2^{(n-1)} \]
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