answer: - (a)![a_n=16+6n](/tex.php?f=a_n=16+6n)
(b) 88 seats
step-by-step explanation:
given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.
thus first term= ![a_1 =22](/tex.php?f=a_1 =22)
second term= ![a_2 =28](/tex.php?f=a_2 =28)
the number of seats in a row continues to increase by 6 with each additional row.
βd= 6
a) given formula : ![a_n=a_1+(n-1)(d)](/tex.php?f=a_n=a_1+(n-1)(d))
![a_n=22+(n-1)6\\\rightarrow\ a_n=22+6n-6\\\rightarrow\ a_n=16+6n](/tex.php?f=a_n=22+(n-1)6\\\rightarrow\ a_n=22+6n-6\\\rightarrow\ a_n=16+6n)
b) let the number of seats (n) = 12
substitute n=12 in the explicit rule formed in (a)
![a_{12} = 16+6\times12\\\rightarrow\ a_{12}=16+72\\\rightarrow\ a_{12}=88\ seats](/tex.php?f=a_{12} = 16+6\times12\\\rightarrow\ a_{12}=16+72\\\rightarrow\ a_{12}=88\ seats)
β΄there are 88 seats in 12 rows.