Question

(1 point) a theater is being designed to seat 1170 people. it is to have 11 seats in the first row, 16 seats in the second row, 21 seats in the third row, and so on. how many rows will this theater need to have? webwork

Answer 1

11, 16, 21 , 26... is arithmetic sequence ,where
a(1)=11,
d=16-11=21-16=5
Sum of arithmetic sequence
Sn=(a(1)+a(n))*n/2
a(n)=a(1)+d(n-1)
S(n)=(a(1)+a(1)+d(n-1))n/2
S(n)=(2a(1)+d(n-1))*n/2
1170=(2*11+5(n-1))*n/2
2*1170=22n+5n²-5n
2*1170=17n+5n²
5n²+17n-2340=0

D=b²-4ac=17²+4*5*2340=47089
n=(-b+/-√D)/2a
n=(-17+/-√47089)10
n=(-17+/-217)/10
We take only positive root, because number of row can be only positive.
n=200/10=20 row