Answer to Question #42500 in Calculus for shasha

Question

An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

1170

735

1230

600

Help me please

Answer 1

Here we have the arithmetic progression.
The general formula is: a_n=a_1+(n-1)d.
As the second row has 2 more seats then the first we can write that d=2.
The thirteenth row has a_30=a_1+(30-1)d=10+29*2=68 seats.
So in the auditorium are a_1+a_2+...+a_30 seats, or

a_1+a_1+d+a_1+2d+a_1+3d+...a_1+29d=30*a_1+sum_(n=0)^(29)[n*d]=300+870=1170.

1170 seats