Type the missing number in this sequence: 4, 16, 64, 256, _____, 4,096

Identify Type: Identify if the sequence is arithmetic or geometric. Each term seems to be multiplied by a common ratio to obtain the next number, indicating that the sequence is geometric.Find Ratio: Find the common ratio in the geometric sequence. Two consecutive terms are 4 and 16. 16 / 4 = 4 Common Ratio: 4Verify Ratio: Verify the common ratio with another pair of consecutive terms. Another pair of consecutive terms is 16 and 64. 64 / 16 = 4 This confirms that the common ratio is indeed 4.Use Ratio: Use the common ratio to find the missing number in the sequence. The number before the missing term is 256. 256 * 4 = 1024 The missing number should be 1024.Verify Number: Verify the found number by checking if the next term after the missing number follows the common ratio. The number after the missing term is 4096. 4096 / 1024 = 4 This confirms that 1024 is the correct missing number in the sequence.

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Type the missing number in this sequence: $\newline$ $4,$ $16,$ $64,$ $256,$ _____, $4,096$

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Math Problems

Algebra 2

Find terms of a geometric sequence

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Q. Type the missing number in this sequence:

\newline

4,

16,

64,

256,

_____,

4,096

Identify Type: Identify if the sequence is arithmetic or geometric. Each term seems to be multiplied by a common ratio to obtain the next number, indicating that the sequence is geometric.
Find Ratio: Find the common ratio in the geometric sequence. $\newline$ Two consecutive terms are $4$ and $16$ . $\newline$ $\frac{16}{4} = 4$ $\newline$ Common Ratio: $4$
Verify Ratio: Verify the common ratio with another pair of consecutive terms. $\newline$ Another pair of consecutive terms is $16$ and $64$ . $\newline$ $64 / 16 = 4$ $\newline$ This confirms that the common ratio is indeed $4$ .
Use Ratio: Use the common ratio to find the missing number in the sequence. $\newline$ The number before the missing term is $256$ . $\newline$ $256 \times 4 = 1024$ $\newline$ The missing number should be $1024$ .
Verify Number: Verify the found number by checking if the next term after the missing number follows the common ratio. $\newline$ The number after the missing term is $4096$ . $\newline$ $4096 / 1024 = 4$ $\newline$ This confirms that $1024$ is the correct missing number in the sequence.