16,33,65,131,261,?
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523
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521
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613
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721
This sequence follows the pattern: multiply by 2 and subtract 1 alternately, or more simply: each number is 2n+1 where n starts at 0. 16=2^4+0, 33=2^5+1, 65=2^6+1, 131=2^7+3, 261=2^8+5. Alternatively: double and subtract 1, then double and subtract 1 again: 16×2-1=31 (not 33), 16×2+1=33, 33×2-1=65, 65×2+1=131, 131×2+1=263 (not 261). The actual pattern is: n×2+1 where n is the previous term. 16×2+1=33, 33×2-1=65, 65×2+1=131, 131×2-1=261, 261×2+1=523.
To solve this question, let's analyze the given sequence of numbers:
16, 33, 65, 131, 261, ?
Looking at the pattern in the sequence, we can see that each number is obtained by multiplying the previous number by 2 and then subtracting 1.
16 * 2 - 1 = 31 33 * 2 - 1 = 65 65 * 2 - 1 = 131 131 * 2 - 1 = 261
Therefore, the next number in the sequence would be:
261 * 2 - 1 = 521
The correct answer is option A) 523.