Write a recursive formula for each sequence given or described below.
it has an explicit formula of f(n) = −3n + 2 for n ≥ 1.

Recursive form of sequence is given by f(n)  = f(n-1) - 3

Step-by-step explanation:

The explicit form of sequence is  given as

       f(n) = −3n + 2

So nth term is given by

            f(n) = −3n + 2

(n-1)th term is given by    

            f(n-1) = −3(n-1) + 2

We have

          f(n) -  f(n-1) = −3n + 2 - (−3(n-1) + 2)

           f(n) -  f(n-1) = −3n + 2 +3(n-1) - 2

           f(n) -  f(n-1) = −3n + 2 +3n -3 - 2

           f(n) -  f(n-1) = -3

           f(n)  = f(n-1) - 3

Recursive form of sequence is given by f(n)  = f(n-1) - 3