In the series given below, one number is wrong. Find the wrong number.
3, 7, 17, 35, 74, 153, 312
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 17
The terms roughly double each step, so compare each term with twice the one before. The rule is multiply by 2 and add 1, 2, 3, 4, ... in turn:
\(3\times2+1=7\)
\(7\times2+2=16\), but the series has 17
\(16\times2+3=35\), which matches the next term
\(35\times2+4=74\)
\(74\times2+5=153\)
\(153\times2+6=312\), the last term
The term after it fits only if the third term is 16; with 17 it would be \(17\times2+3=37\). So 17 does not fit the series.