To find the next term in the sequence \(-324, 108, -36, 12...\), we can look for a pattern in how the terms are changing.
- Calculate the ratio of consecutive terms:
- From \(-324\) to \(108\): \[ \frac{108}{-324} = -\frac{1}{3} \]
- From \(108\) to \(-36\): \[ \frac{-36}{108} = -\frac{1}{3} \]
- From \(-36\) to \(12\): \[ \frac{12}{-36} = -\frac{1}{3} \]
It appears that each term is being multiplied by \(-\frac{1}{3}\).
- Applying the ratio to find the next term:
- The last term is \(12\). To find the next term, we multiply \(12\) by \(-\frac{1}{3}\): \[ 12 \times -\frac{1}{3} = -4 \]
Therefore, the next term in the sequence is \(-4\).
The answer is \(-4\).