Determine the most probable next term in the following list of numbers. \[ 1,2,4,8,16 \] \( 1,2,4,8,16, \square \) (Type an integer or a simplified fraction.)

To determine the most probable next term in the sequence \( 1, 2, 4, 8, 16 \), we can analyze the pattern of the numbers. 1. **Identify the pattern**: - The sequence starts with \( 1 \) and each subsequent term is obtained by multiplying the previous term by \( 2 \): - \( 1 \times 2 = 2 \) - \( 2 \times 2 = 4 \) - \( 4 \times 2 = 8 \) - \( 8 \times 2 = 16 \) 2. **Continue the pattern**: - Following this pattern, the next term would be: - \( 16 \times 2 = 32 \) Thus, the most probable next term in the sequence is \( 32 \). The complete sequence is: \[ 1, 2, 4, 8, 16, 32 \] Therefore, the answer is \( 32 \).