Here is a number pattern with a missing number: 2, 8, 32, X, 512, and 2048. What is the missing number represented by X?

Here is a number pattern with a missing number: 2, 8, 32, X, 512, and 2048. What is the missing number represented by X?

• A. 64
• B. 128
• C. 256
• D. 512

Answer: (B)

To find the missing number in the sequence, it is essential to identify the pattern of the numbers given. The sequence is as follows: 2, 8, 32, X, 512, 2048. Let's analyze the relationship between each of the numbers. Notably, each number can be expressed as a power of 2: - \(2 = 2^1\) - \(8 = 2^3\) - \(32 = 2^5\) - \(512 = 2^9\) - \(2048 = 2^{11}\) Observing the exponents, they follow a specific pattern: 1, 3, 5, ?, 9, 11. The exponents increase by 2 each time. Following this pattern, the exponent that corresponds to the missing number should be \(7\) (between \(5\) and \(9\)). Now, calculating \(2^7\) gives us: \[ 2^7 = 128 \] Thus, the missing number \(X\) is indeed 128. This aligns with the established pattern where each number in the sequence corresponds to increasing powers of 2, maintaining a consistent

To find the missing number in the sequence, it is essential to identify the pattern of the numbers given. The sequence is as follows: 2, 8, 32, X, 512, 2048.

Let's analyze the relationship between each of the numbers. Notably, each number can be expressed as a power of 2:

• (2 = 2^1)

• (8 = 2^3)

• (32 = 2^5)

• (512 = 2^9)

• (2048 = 2^{11})

Observing the exponents, they follow a specific pattern: 1, 3, 5, ?, 9, 11. The exponents increase by 2 each time. Following this pattern, the exponent that corresponds to the missing number should be (7) (between (5) and (9)).

Now, calculating (2^7) gives us:

[

2^7 = 128

]

Thus, the missing number (X) is indeed 128. This aligns with the established pattern where each number in the sequence corresponds to increasing powers of 2, maintaining a consistent