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Type the missing number in this sequence: $\newline$ $4$ , $16$ , $64$ , $256$ , $\_$

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Geometric sequences

Full solution

Q. Type the missing number in this sequence:

\newline

4

,

16

,

64

,

256

,

\_

Identify pattern: Identify the pattern in the sequence. $\newline$ We notice that each number in the sequence is a power of $4$ : $4^1$ , $4^2$ , $4^3$ , $4^4$ . To find the next number, we should continue this pattern.
Determine exponent: Determine the exponent for the next number in the sequence. The sequence follows the pattern of $4$ raised to the power of $n$ , where $n$ is the position in the sequence. The next position would be $n = 5$ .
Calculate next number: Calculate the next number in the sequence using the pattern. $\newline$ The next number would be $4$ raised to the power of $5$ : $4^5$ .
Perform calculation: Perform the calculation for $4^5$ . $4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024$

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