Q:

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

Accepted Solution

A:
Answer:Recursive form of sequence is given by f(n)  = f(n-1) - 3Step-by-step explanation:The explicit form of sequence is  given as        f(n) = −3n + 2So nth term is given by             f(n) = −3n + 2 (n-1)th term is given by                 f(n-1) = −3(n-1) + 2We 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) - 3Recursive form of sequence is given by f(n)  = f(n-1) - 3