The missing term in the series 1, 4, 27, 16, ?, 36, 343, ... is
125
To find the missing term in the sequence 1, 4, 27, 16, ?, 36, 343, we need to analyze the pattern involved. Observation shows that the series is alternating between cubes and squares:
- The first term is 1, which is \(1^3\).
- The second term is 4, which is \(2^2\).
- The third term is 27, which is \(3^3\).
- The fourth term is 16, which is \(4^2\).
- The fifth term is missing. If we follow the pattern, this should be a cube. The term should be \(5^3\), which equals 125.
- The sixth term is 36, which is \(6^2\).
- The seventh term is 343, which is \(7^3\).
Therefore, the missing term in the series is 125, which matches the pattern of alternating cubes and squares.
Thus, the correct answer is 125.
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