Question

Auditoriums are often designed so that are fewer seats per row for rows closer to the stage. Suppose you are sitting in row 18 in an auditorium and notice that there are 73 seats in your row. It appears the row in front of you has 70 seats and the row behind you has 76 seats. Suppose this pattern continues throughout the auditorium.
a) How many seats are in the first row?

b) How many seats are in the 30th row?

c) Write an explicit formula for the sequence where a, is the number of seats in the nh row

Answer 1

Answer:

(a) $22$ (b) $109$

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 $18$ in an auditorium and notice that there are $73$ seats in your row. It appears the row in front of you has $70$ seats and the row behind you has $76$ 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 $30th$ row?

SOLUTION:

total seats in $row_{19}=76$

total seats in $row_{18}$ $=73$

total seats in $row_{17}=70$

as it clearly form an A.P. with $d=76-73=3$

(a)

let total seat in first row be $a$

as total seats in $row_{18}=73$

$row_{18}=a+(n-1)d$

$73=a+17\times3$

$a=22$

total seats in first row are $22$

(b)

total seats in $30th$ be $x$

$x=row_{1}+(30-1)3$

$x=22+29\times3$

$x=109$

total seats in $30th$ row  are $109$