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Type the missing number in this sequence: $\newline$ $1$ , $\_$ , $16$ , $64$ , $256$ , $1,024$

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Geometric sequences

Full solution

Q. Type the missing number in this sequence:

\newline

1

,

\_

,

16

,

64

,

256

,

1,024

Identify Pattern in Sequence: We need to identify the pattern in the sequence. Let's look at the relationship between the numbers we know: $1, 16, 64, 256$ , and $1,024$ .
Recognize Power of $2$ : We can see that each number is a power of $2$ . Specifically, $1$ is $2^0$ , $16$ is $2^4$ , $64$ is $2^6$ , $256$ is $2^8$ , and $1,024$ is $2^{10}$ .
Determine Missing Power: To find the missing number, we need to determine the power of $2$ that fits in the sequence between $2^0$ and $2^4$ . The missing power of $2$ should be $2^2$ , which is $4$ .
Verify Pattern Continuity: Let's check if the pattern holds. The sequence should be powers of $2$ in increasing order: $2^0$ , $2^2$ , $2^4$ , $2^6$ , $2^8$ , $2^{10}$ . This means the missing number is $2^2$ , which is $4$ .

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