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Type the missing number in this sequence: $\newline$ $1$ , $4$ , $\_$ , $64$ , $256$

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Geometric sequences

Full solution

Q. Type the missing number in this sequence:

\newline

1

,

4

,

\_

,

64

,

256

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. $\newline$ Looking at the sequence, it seems that each term might be a power of a certain number because $1$ , $64$ , and $256$ are all powers of $2$ ( $2^0$ , $2^6$ , and $2^8$ respectively). This suggests that the sequence is geometric.
Find Common Ratio: Identify the common ratio. $\newline$ To find the common ratio, we can use the terms we know. Since $256$ is $2^8$ and $64$ is $2^6$ , we can divide $256$ by $64$ to find the common ratio. $\newline$ $256 / 64 = 4$ $\newline$ Common Ratio: $4$
Find Missing Number: Find the missing number. $\newline$ Since the common ratio is $4$ and the number before the missing term is $4$ , we can multiply $4$ by the common ratio to find the missing term. $\newline$ $4 \times 4 = 16$ $\newline$ Missing Number: $16$

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