Question
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.)
Ask by Bryant Grant. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The next term is 32.
Solution
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 \( 32 \).
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Simplify this solution Extra Insights
The sequence given is a clear progression of powers of 2: - \(1\) is \(2^0\), - \(2\) is \(2^1\), - \(4\) is \(2^2\), - \(8\) is \(2^3\), - \(16\) is \(2^4\). Following this pattern, the next term in the sequence would be \(2^5\), which is \(32\). Thus, the next term is \(32\).
