Question

In a section of a baseball stadium, there are 11 seats in the first row. There are 15 seats in the second row, 19 seats in the third row, and 23 seats in the fourth row.

If the number of seats in each row follows the pattern described above, which recursive function defines the number of seats in the Nth row?

Answer 1

f(1)=11

f(n)=f(n-1)+4, for n >2

Answer 2

`a_(n)` =
`a_(n-1)` + 4

this is an arithmetic sequence with n th term formula

`a_(n)` =
`a_(1)` + (n - 1)d

where d is the common difference and
`a_(1)` the first term

here d = 23 - 19 = 19 - 15 = 4 and
`a_(1)` = 11

`a_(n)` = 11 + 4(n - 1 ) = 11 + 4n - 4 = 4n + 7 ← explicit formula

A recursive formula allows us to find any term from the previous term.

`a_(n)` =
`a_(n-1)` + 4 ← recursive function