Question

Find the missing term
1, 4, 27, 16, ?, 36, 343

• A. 25
• B. 877
• C. 120
• D. 125

Answer 1

The Correct Option is D

The given sequence is: 1, 4, 27, 16, ?, 36, 343.

To find the missing term, we must identify any patterns in the sequence:

1. Observe that 1, 27, and 343 fit the pattern of cubes: \((1^3 = 1)\), \((3^3 = 27)\), \((7^3 = 343)\).

2. Separately, 4, 16, and 36 fit the pattern of squares: \((2^2 = 4)\), \((4^2 = 16)\), \((6^2 = 36)\).

This suggests two interleaved patterns: one of squares, the other of cubes.

Following this, the pattern goes:

\(1^3\), \(2^2\), \(3^3\), \(4^2\), \(5^3\), \(6^2\), \(7^3\).

The missing term aligns with \(5^3\), which calculates as:

\(5^3 = 5 \times 5 \times 5 = 125\).

Thus, the sequence correctly features 125 as the missing term.

Therefore, the missing term is 125.