[tex]a_{n}[/tex] = 9n + 63
generate the first few terms using the recursive equation
f(1) = 72
f(2) = 72 + 9 = 81
f(3) = 81 + 9 = 90
f(4) = 90 + 9 = 99
the sequence is 72, 81, 90, 99, .....
This is an arithmetic sequence whose n th term formula is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
where [tex]a_{1}[/tex] is the first term and d the common difference
d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and [tex]a_{1}[/tex] = 72
[tex]a_{n}[/tex] = 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula
