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

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