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Type the missing number in this sequence:\newline44, 1616, 6464, _\_, 1,0241,024, 4,0964,096

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Full solution

Q. Type the missing number in this sequence:\newline44, 1616, 6464, _\_, 1,0241,024, 4,0964,096
  1. Identify Sequence Type: Is the given sequence geometric or arithmetic? Each term seems to be multiplied by a common ratio to obtain the next number. The given sequence appears to be geometric.
  2. Find Common Ratio: Find the common ratio in the geometric sequence. Two consecutive terms are 44 and 1616. 164=4\frac{16}{4} = 4 Common Ratio: 44
  3. Multiply by Common Ratio: We multiply each term by the common ratio to get the next term. \newlineSequence: 4,16,64,_,1,024,4,0964, 16, 64, \_, 1,024, 4,096 \newlineCommon Ratio: 44 \newlineFind the missing number in the sequence. \newlineThe number before the missing term is 6464. \newline64×4=25664 \times 4 = 256 \newlineMissing Number: 256256
  4. Find Missing Number: Verify the found number by checking if the next term after the missing number, when divided by the missing number, equals the common ratio. \newline1,024/256=41,024 / 256 = 4 \newlineThe common ratio is consistent.

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