What is explicit formula?

An explicit formula, also known as a general formula, is a mathematical formula that describes a sequence or relationship between variables in a straightforward, easily-understandable form. It provides a direct way to calculate the value of a term in a sequence or the relationship between variables without needing to know the previous terms.

For example, the explicit formula for the Fibonacci sequence is given by the formula F_n = (1/sqrt(5)) * ((1+sqrt(5))/2)^n - (1/sqrt(5)) * ((1-sqrt(5))/2)^n, where F_n represents the nth term in the sequence.

Explicit formulas are often used in mathematics, physics, engineering, and other fields to model relationships between variables, make predictions, and solve problems. They are valuable tools for analyzing and interpreting data, as well as making calculations efficiently.