How many terms are there in the series 201, 208, 215, ....., 369?

The correct answer is Option (3) → 25

The terms go up by 7 each time (201, 208, 215, ...), so the series is an arithmetic progression with \(a=201\) and \(d=7\). The \(n\)th term is \(a+(n-1)d\), and setting it equal to the last term 369 gives the number of terms.

• Last term as the \(n\)th term: \(201+(n-1)\times7=369\)

• Total rise from the first term to the last: \((n-1)\times7=168\)

• Number of steps of 7: \(n-1=24\), so the number of terms is \(n=25\)