Find the A.P. whose 3rd term is 18 and 12th term is 72.

The correct answer is Option (1) → 6, 12, 18, ...

The \(n\)th term of an A.P. is \(a+(n-1)d\). From the 3rd term to the 12th term there are 9 common differences.

• \(9d=72-18=54\), so \(d=6\)

• 3rd term: \(a+2d=18\), so \(a=18-12=6\)

• The A.P.: 6, 12, 18, …