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 ...

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 \ ...

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 ...

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 ...

Every positive sequence generated by the Fibonacci recurrence relation diverges to infinity. However, every positive sequence generated by the square root of the Fibonacci recurrence relation ...