What is the next number in the sequence 1, 4, 9, 16?

What is the next number in the sequence 1, 4, 9, 16?

• A. 20
• B. 24
• C. 25
• D. 30

Answer: (C)

The sequence given is 1, 4, 9, 16, which represents the squares of consecutive integers: - 1 is \(1^2\) - 4 is \(2^2\) - 9 is \(3^2\) - 16 is \(4^2\) Following this pattern, the next number in the sequence would be \(5^2\), which equals 25. This shows that each number in the sequence is formed by squaring the next integer in line. Therefore, the next number, which is 25, aligns perfectly with the established pattern of perfect squares. The other numbers listed do not fit into this recognizable mathematical structure of the sequence.

The sequence given is 1, 4, 9, 16, which represents the squares of consecutive integers:

• 1 is (1^2)

• 4 is (2^2)

• 9 is (3^2)

• 16 is (4^2)

Following this pattern, the next number in the sequence would be (5^2), which equals 25. This shows that each number in the sequence is formed by squaring the next integer in line.

Therefore, the next number, which is 25, aligns perfectly with the established pattern of perfect squares. The other numbers listed do not fit into this recognizable mathematical structure of the sequence.