1. In your own words, explain the difference between a recursive formula and a explicit formula. (Hint: USE YOUR NOTES to help you) 2. Is the following sequence a recursive or explicit formula? Why? (4 points)

Answer 1

1. A recursive formula defines each term of a sequence based on the previous term(s). In other words, it tells you how to find a new term using the values of earlier terms in the sequence. For example, a recursive formula for the Fibonacci sequence states that each term is the sum of the two preceding terms.

An explicit formula, on the other hand, provides a direct way to calculate the nth term of a sequence without needing to refer to previous terms. This means that you can find any term in the sequence just by plugging in its position (n) into the formula. For example, an explicit formula for the nth Fibonacci number gives a specific calculation to find that term directly.

2. To determine whether a given sequence is represented by a recursive or explicit formula, I would need to see the specific formula or definition of the sequence in question. If the formula references previous terms to find a new term, it is recursive. If it allows for the straight calculation of a term based solely on its position in the sequence, it is explicit. Please provide the sequence or the formula you’re referring to for a more specific analysis!