In an arithmetic sequence, the successive terms differ by a common difference.
The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence
d represents the common difference
n represents the number of terms(figure)
From the information given,
a = 5
second term, T2 = 9
Third term, T3 = 13
d = T2 - T1 = T3 - T2 = 9 - 5 = 13 - 9
d = 4
Tn = 89
Therefore,
89 = 5 + (n - 1)4
89 = 5 + 4n - 4
89 = 5 - 4 + 4n
89 = 1 + 4n
4n = 89 - 1 = 88
n = 88/4
n = 22
The 22nd figure has 89 tiles