Discussion
Insert the missing number 15, 31, 63, 127, 255, (....)
Answer: B
Each term is double the previous plus one.
\[ 15 \times 2 + 1 = 31,\quad 31 \times 2 + 1 = 63,\quad 63 \times 2 + 1 = 127 \]
\[ 127 \times 2 + 1 = 255,\quad 255 \times 2 + 1 = \mathbf{511} \]
Equivalently every term is \( 2^{n} - 1 \): 15, 31, 63, 127, 255, 511. The 513 on offer is \( 2^{9} + 1 \), one on the wrong side.
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