row 1 = 49
row 2 = 53
row 3 = 57
this is an arithmetic sequence
formula for the last term in an arithmetic sequence is l = a + (n-1)d
a is the first number in the sequence
l is the last number in the sequence
n is the number of terms in the sequence.
for the part of the sequence that is given to you, we get:
a = 49
n = 3
d = 4
use this formula to find the number of the last term in the sequence.
you get l = 49 + 2*4 = 49 + 8 = 57
as you can see, the last term in the sequence is 57 as given so the formula is good.
we know it's an arithmetic sequence because it has a common difference which is 4.
the number of seats in row 18 would be given by the same formula.
l = a + (n-1) * d which becomes l = 49 + 17*4 which becomes l = 49 + 68 which becomes l = 117
if you wanted to take the trouble of actually plotting out the sequence, it would look like this:
i x.i
1 49
2 53
3 57
4 61
5 65
6 69
7 73
8 77
9 81
10 85
11 89
12 93
13 97
14 101
15 105
16 109
17 113
18 117
i is the row number
x.i is the number of seats in that row.
this is not a geometric sequence because you don't have a common ratio.
the formula for a geometric sequence is l = a*r^(n-1)
an example of a geometric sequence would be:
1
2
4
8
the common ratio is 2 because each number is 2 times the number before it.
in this geometric sequence, the 4th number in the sequence would be found using the formula of l = 1*2^3 which becomes l = 1*8 which becomes l = 8.
since the 4th number in the sequence is 8, the formula works.
in your problem there is no common ratio.
53/49 = 1.0816326...
57/53 = 1.0754716...
there is, however, a common difference of 4.