Question

A sequence can be defined by the explicit formula an=5-3n. Which recursive formula represents the same sequence of numbers?

Answer 1

First term: a1 = 5 − 3(1) = 2. Each step subtracts 3, so

a1 = 2, and for n ≥ 2: a_n = a_{n-1} − 3.

(If you prefer indexing from 0: a0 = 5 and for n ≥ 1, a_n = a_{n-1} − 3.)