An auditorium with 30 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, what is the maximum number of students that can be seated for an exam?
Nice effort guest, you just messed up a little with how many students can be seated in each odd row. 
How many seats are there in the audirtorium. I do not need to find this but I want to check my answer above the one above. S30=30/2(20+29*1)=15*49=735 
A match
5 people first row out of 10 seats
6 people second row out of 11 seats
6 people second row out of 12 seats
7 people second row out of 13 seats
7 people second row out of 14 seats
....
How many seats are in the 30th row?
\(T_{30}=10+29*1=39seats\)
20 people 30th row out of 39 seats
Number of people
= (5+6+.....+19)+(6+7+...+20)
= 5+2(6+7+...+19)+20
=25 + 2[n/2(a+L)]
=25 + 2[ 14/2(6+19)]
=25 + 14*(25)
=25 + 350
=375
A total of 375 students can be seated in the auditorium :)
+118725 
