Question

Write a recursive formula for each sequence given or described below.

It has an explicit formula of f(n) = −3n + 2 for n ≥ 1.

Answer 1

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

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