Homework \( 1 \leftarrow \quad \) Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \( 1,2,1,4,1,8,1 \),

If we look closely at this sequence, we can identify a repeating pattern: every second number is consistently "1", while the first, third, and fifth positions follow a pattern of doubling (2, 4, 8). Therefore, following the established pattern, the next number after "1" would be \( 1 \), and the next number in the doubling sequence would be \( 16 \). So, we can continue the sequence as \( 1, 2, 1, 4, 1, 8, 1, 16, 1 \). Now, if we take a different angle, we could also interpret the sequence where "1" seats itself amidst powers of 2. In this context, we see it alternate: \( 1, 2^1, 1, 2^2, 1, 2^3, 1 \). Hence, the next logical \(n^{th}\) term would involve \(2^4\) after another "1," which gives us \( 1, 2, 1, 4, 1, 8, 1, 16 \). What fun ways our numbers can dance!