1. In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a

row continues to increase by 6 with each additional row.

(a) Write an iterative 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 100 seats. Show your work.

a) The sequence is 22 , 28 , 34, 40 ,46 , …..

b) The 14 term of the sequence has 100 seats

Step-by-step explanation:

In an auditorium, there are 22 seats in the first row and 28 seats in the second row,...

The sequence is 22 , 28 , 34, 40 ,46 , …..

we observe that the difference between 28 and 22 is '6'

between 34 and 28 is '6'

between 40 and 34 is '6'  and so on

The given sequence is arithmetic progression

Here d = 6 , a= 22

The 'n' th term of the sequence

b) Given and find n =?

n = 14

The 14 t h row has 100 seats

Verification:-

substitute n = 14 , a=22 and d=6

(I WILL PROVIDE A PIC OF TABLE FOR BETTER UNDERSTANDING)

A)(r-1)

B(r – 1)

100 = 22 + 6(r – 1)  

100 = 22 + 6r – 6  

100 = 16 + 6r  

r = 14

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