Question

7) The recursive formula for a function is given as: f(0) = 3,f(x) = f(x - 1) + 8

a) Geometric or Arithmetic? Explain how you know.

b) Linear or Exponential? Explain how you know

Answer 1

a) Arithmetic

b) Linear.

Explanation:

The recursive formula for a function is given as:

`f(0) = 3,\ f(x) = f(x - 1) + 8`

Find first terms in this sequence:

`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\\ \\...`

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.