A recurrence relation is an equation that specifies one (or more) known terms in a sequence and then a rule for calculating the next term in the sequence. If the initial value in a recurrence relation ...

where $a_0,\ a_1,\ a_2,\ ...\ a_k, c_0,\ c_1,\ c_2,\ ...\ c_k \in \mathbb{R}$ (although these can be complex numbers $\mathbb{C}$ as well, but for simplicity we keep ...

Remember that a recurrence relation is a sequence that gives you a connection between two consecutive terms. These two terms are usually \({U_{n + 1}}\) and \({U_n}\). However they could be given as \ ...

Polynomial equations have long served as a cornerstone of mathematical analysis, offering a framework to understand functions, curves, and dynamic systems. In recent years, the study of these ...

The general terms of third order recursive sequences are expressed in terms of iterative formulas which do not depend on the explicit solution of the auxiliary equations. Some identities associated ...

A sequence is defined by the recurrence relation \({U_n} = m{U_{n - 1}} + c\) Find the values of \(m\) and \(c\) if \({U_1} = - 3\), \({U_2} = 7\) and \({U_3} = 10 ...