Question

 WILL GIVE BRAINLIEST ANSWER PLEASE HELP In a theater there are 12 seats on the first row and 16 seats in the second row. the number of seats in a row continues to increase by 4 with each additional row

a. write and iterative (explicit rule to model the sequence formed by the number of seats in each row. Show your work

b. use the rule to determine which row has 60 seats. Show your work

Answer 1

(a) $a_{n}$ = 4n + 8

(b) row 13 has 60 seats

(a)

the sequence of seats is an arithmetic sequence whose n th term is

$a_{n}$ = $a_{1}$ + (n - 1 )d

where $a_{1}$ is the first term and d the common difference

here the sequence is 12, 16, ....

with $a_{1}$ = 12 and d = 16 - 12 = 4, thus

$a_{n}$ = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8

(b)

calculate the number of rows n when 60 seats

solve 4n + 8 = 60 ( subtract 8 from both sides )

4n = 52 ( divide both sides by 4 )

n = 13 ← number of rows