Which term of the A.P. 3, 7, 11, ..., 147 is its middle term?

The correct answer is Option (2) → 19^th

An A.P. with an odd number of terms \(n\) has one middle term, the \(\left(\frac{n+1}{2}\right)\)th term. So first find the number of terms from \(a_n=a+(n-1)d\).

• First term \(a=3\), common difference \(d=4\), last term 147

• \(147=3+(n-1)\times4\)

• \(n-1=36\), so there are \(n=37\) terms

• Middle term: \(\displaystyle\frac{37+1}{2}=19\), the 19^th term