3. 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.
(b) use the rule to determine which row has 100 seats. show your work.

a) s+6

b)

22+6=2828+6=3434+6=4040+6=4646+6=5252+6=5858+6=6464+6=7070+6=7676+6=8282+6=+6=9494+6=100

So we look at the formula un = a + (n-1)d
un is the amount of seats
n is the nth term aka row number
a is the original sequence/row number
d is the difference between each term
so in this a=22 d=6 and n can remain as n because we are simply formjng a rule
lets put these in the equation
un=22+(n-1)(6)
this is your answer to part a
however
lets double check that this is correct, we'll try putting it into the second term
un=a+(n-1)d
u2=22+(2-1)(6)
u2=22+6
u2=28
as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b
un=a+(n-1)
its asking us to find a row with 100 seats.
remember un was the amount of seata so all we do is substitute this in.
un=100 a=22 d=6
un=a+(n-1)d
100=22+(n-1)(6)
so now we simplify to find n which is the row number.
100-22=22+(n-1)(6)-22
78=(n-1)(6)
78/6=(n-1)(6)/6
13=n-1
13+1=n-1+1
14=n
so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand : d

91 degrees

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