Suppose you know the perimeter of n octagons arranged as shown. what would you do to find the perimeter if 1 more octagon was added?

As shown in the figures given :

For Figure 1 : perimeter = 8 units   [As can be seen in the figure]

For figure 2(with 2 octagons) : perimeter = 8 × 2 - 1 = 15 units    [since 1 side is common ]

For figure 2(with 3 octagons) : perimeter = 8 × 3 - 2 = 22 units  [since 2 sides is common ]

If one more octagon is added

then perimeter = 8 × 4 - 3 = 29 units    [since 3 sides will be common ]

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