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Type the missing number in this sequence:\newline4,4, 16,16, 64,64, 256,256, _____, 4,0964,096

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Q. Type the missing number in this sequence:\newline4,4, 16,16, 64,64, 256,256, _____, 4,0964,096
  1. 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.
  2. Find Ratio: Find the common ratio in the geometric sequence.\newlineTwo consecutive terms are 44 and 1616.\newline164=4\frac{16}{4} = 4\newlineCommon Ratio: 44
  3. Verify Ratio: Verify the common ratio with another pair of consecutive terms.\newlineAnother pair of consecutive terms is 1616 and 6464.\newline64/16=464 / 16 = 4\newlineThis confirms that the common ratio is indeed 44.
  4. Use Ratio: Use the common ratio to find the missing number in the sequence.\newlineThe number before the missing term is 256256.\newline256×4=1024256 \times 4 = 1024\newlineThe missing number should be 10241024.
  5. Verify Number: Verify the found number by checking if the next term after the missing number follows the common ratio.\newlineThe number after the missing term is 40964096.\newline4096/1024=44096 / 1024 = 4\newlineThis confirms that 10241024 is the correct missing number in the sequence.

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