How many terms are there in the A.P. 3, 7, 11, ....... 407 ?

The correct answer is Option (4) → 102

The \(n\)th term of an A.P. is \(a+(n-1)d\), where \(a\) is the first term and \(d\) the common difference. Here \(a=3\), \(d=7-3=4\) and the last term is 407.

• The last term is the \(n\)th: \(3+(n-1)\times4=407\)

• \((n-1)\times4=404\), so \(n-1=101\)

• Number of terms: \(n=102\)

Tip: Number of terms \(=\) (last term \(-\) first term) \(\div\) common difference \(+\,1\). Leaving out the +1 gives 101, Option (2).