Complete the series, 3, 12, 27, 48, 75, 108, ?

The correct answer is Option (1) → 147

Each term is three times a perfect square: the terms are \(3\times n^{2}\) for \(n=1,2,3,\ldots\)

• \(3=3\times1^{2}\), \(12=3\times2^{2}\), \(27=3\times3^{2}\), \(48=3\times4^{2}\)

• \(75=3\times5^{2}\), \(108=3\times6^{2}\)

• Next term \(=3\times7^{2}=3\times49=147\)

The differences between the terms lead to the same answer: they are 9, 15, 21, 27, 33, growing by 6 each time, so the next difference is 39 and the next term is \(108+39=147\).