Answer:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 3
Step-by-step explanation:
the coordinates of the points are
(1, - 6 ), (2, - 3 ), (3, 0 ), (4, 3 ), (5, 6 )
consider the values of y
- 6, - 3, 0, 3, 6
there is a common difference between consecutive terms, that is
- 3 - (- 6) = 0 - (- 3) = 3 - 0 = 6 - 3 = 3
this indicates the sequence is arithmetic with recursive rule
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + d ( d is the common difference )
here d = 3 , then recursive formula is
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 3 ; with a₁ = - 6
