Answer:
a) Arithmetic
b) Linear.
Step-by-step explanation:
The recursive formula for a function is given as:
[tex]f(0) = 3,\ f(x) = f(x - 1) + 8[/tex]
Find first terms in this sequence:
[tex]f(0)=3\\ \\f(1)=f(1-1)+8=f(0)+8=3+8=11\\ \\f(2)=f(2-1)+8=f(1)+8=11+8=19\\ \\f(3)=f(3-1)+8=f(2)+8=19+8=27\\ \\...[/tex]
As you can see, each next term differs from the previous term by 8 (is 8 greater than the previous)m so this recursive formula represents arithmetic sequence.
Each arithmetic sequence is always linear.
