Algebra-1

To determine whether the formula =  + 3 with = 5 is explicit or recursive, let's break down what each type of formula means and then apply these concepts to the given formula.

Explicit Formula: An explicit formula provides a direct calculation for the n-th term of a sequence using  alone. You can compute  directly without referring to any previous terms in the sequence.

Recursive Formula: A recursive formula defines each term in the sequence based on one or more previous terms. It typically involves:

A base case (or initial condition) that provides the value of the first term (or terms).

A recursive rule that shows how to calculate  from the previous term(s), such as , and possibly other earlier terms.

Analysis of  =  + 3 with = 5

Recursive Formula: The formula =