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for the given number patterns are:

  • $2\times 2-1=3$
  • $3\times 2-1=5$
  • $5\times 2-1=9$
  • $9\times 2-1=17$
  • $17\times 2-1=33$
  • $33\times 2-1=65$
  • $65\times 2-1=129$
  • $129\times 2-1=257$

So the missing number is $257$, Option (C) is correct.

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