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?

Correct answer: 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.