Question

A theater has 35 rows of chairs. The first row has 20 chairs, the second has 22, the third has 24, and so on. In total, the theater seats _____ people.

Answer 1

            Here we have an arithmetic sequence:
            a 1 = 20,  d = 2,  n = 35
            S n = n/2 * ( a 1 + a n )
            a 35 = a 1 + 34 d = 20 + 34 * 2 = 20 + 68 = 88
            S 35 = 35/2 * ( 20 + 88 ) = 35 / 2 * 108 = 1,890
            Answer:  In total, the theater seats 1,890 people