Find the 18th and nth terms of the A.P. given by:8, 13, 18, ...

The correct answer is Option (2) → \(93, 3+5n\)

The \(n\)th term of an A.P. with first term \(a\) and common difference \(d\) is \(a_n=a+(n-1)d\). Each term is the first term plus as many common differences as there are steps from it. Here \(a=8\) and \(d=13-8=5\).

• 18th term, 17 steps of 5 after the first term: \(8+17\times5=93\)

• \(n\)th term, \(n-1\) steps of 5 after the first term: \(8+(n-1)\times5=3+5n\)