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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step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be