Answer :
Answer:
(a) [tex]22[/tex] (b) [tex]109[/tex]
Step-by-step explanation:
GIVEN: Auditoriums are often designed so that are fewer seats per row for rows closer to the stage. Suppose you are sitting in row [tex]18[/tex] in an auditorium and notice that there are [tex]73[/tex] seats in your row. It appears the row in front of you has [tex]70[/tex] seats and the row behind you has [tex]76[/tex] seats. Suppose this pattern continues throughout the auditorium.
TO FIND: a) How many seats are in the first row b) How many seats are in the [tex]30th[/tex] row?
SOLUTION:
total seats in [tex]row_{19}=76[/tex]
total seats in [tex]row_{18}[/tex] [tex]=73[/tex]
total seats in [tex]row_{17}=70[/tex]
as it clearly form an A.P. with [tex]d=76-73=3[/tex]
(a)
let total seat in first row be [tex]a[/tex]
as total seats in [tex]row_{18}=73[/tex]
[tex]row_{18}=a+(n-1)d[/tex]
[tex]73=a+17\times3[/tex]
[tex]a=22[/tex]
total seats in first row are [tex]22[/tex]
(b)
total seats in [tex]30th[/tex] be [tex]x[/tex]
[tex]x=row_{1}+(30-1)3[/tex]
[tex]x=22+29\times3[/tex]
[tex]x=109[/tex]
total seats in [tex]30th[/tex] row are [tex]109[/tex]