To find an equation that describes the sequence \(-1, -2, -4, \ldots\), we first need to analyze the pattern.
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Identify the pattern:
- The sequence can be seen as:
- \(a_1 = -1\)
- \(a_2 = -2\)
- \(a_3 = -4\)
- The sequence can be seen as:
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Determine the relationship:
- The first term is \(-1\).
- The second term is \(-2\) which can be viewed as \(-1 \times 2^1\).
- The third term is \(-4\) which can be viewed as \(-1 \times 2^2\).
We can see that:
- \(a_n = -1 \times 2^{n-1}\).
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Write the equation: Therefore, the equation that describes the sequence is:
\[ a_n = -1 \cdot (2)^{n-1} \]
So, you would fill in the blanks as follows:
\[ a_n = -1 \cdot (2)^{n-1} \]