Find the next number in the sequence. 2, 6, 14, 30, 62, ?
126
This is a number-series problem in which each term is generated from the one before it by a fixed rule combining multiplication and addition.
The sequence is \(2,\ 6,\ 14,\ 30,\ 62,\ ?\).
Test the rule “double the previous term and add 2”.
\(2 \times 2 + 2 = 6\) and \(6 \times 2 + 2 = 14\).
\(14 \times 2 + 2 = 30\) and \(30 \times 2 + 2 = 62\), so the rule fits every step.
Apply the same rule to the last term: \(62 \times 2 + 2 = 124 + 2 = 126\).
Notice too that each term is 2 less than a power of 2 \((4-2,\ 8-2,\ 16-2,\ 32-2,\ 64-2,\ 128-2)\), which confirms 126.
Hence the next number in the sequence is 126.
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