To find the equation that describes the sequence \(-24, 48, -96\), we can start by examining the first few terms:
- \( a_1 = -24 \)
- \( a_2 = 48 \)
- \( a_3 = -96 \)
Identifying the Pattern
Let's observe how each term relates to the position \( n \):
- The first term is \(-24\).
- The second term is \( 48\) which is \(-24(−2)\).
- The third term is \(-96\) which is \(48(−2)\) or \(-24(−4)\).
Finding a Formula
There appears to be a pattern in the signs and the magnitudes. Each term seems to alternate signs and is multiplied by a factor related to \( (-2) \).
From this observation, we can conclude that with each term, the value is multiplied by \(-2\) raised to the power of \( n - 1\).
General Formula
The general formula for this sequence can be expressed as:
\[ a_n = -24 \cdot (-2)^{n-1} \]
Final Answer
Thus, the equation to describe the sequence is:
\[ a_n = -24(-2)^{n-1} \]