In an auditorium, the seats in rows are (30,36,42,\ldots). How many seats are there from the (25)th row to the (50)th row?

6474

This is an AP with first term 30 and common difference 6. The 25th row has \(30+24\times6=174\) seats, and the 50th row has \(30+49\times6=324\) seats. There are \(50-25+1=26\) rows from the 25th through the 50th row. Therefore, the sum is \(\frac{26}{2}(174+324)=6474\). Both the 25th and 50th rows must be included, so the number of terms is 26, not 25. Exam tip: for a sum over an inclusive range, use last position minus first position plus 1 for the number of terms.

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.