Which number will replace the question mark (?) in the following series?
0, 4, 18, 48, 100, ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 180
The differences 4, 14, 30, 52 do not show the rule quickly, so compare each term with the squares 1, 4, 9, 16, 25. Each term is a square multiplied by one less than its root, that is \(n^2\times(n-1)\):
\(1^2\times0=0\), \(2^2\times1=4\)
\(3^2\times2=18\), \(4^2\times3=48\)
\(5^2\times4=100\)
\(6^2\times5=36\times5=180\)
So the missing number is 180.