In this chapter we discuss sequences which are defined by certain recurrence relations called difference equations. In general, they are divided into two different types; the finite and the infinite sequences. The finite sequences in turn are separated into two different cases; namely the periodic sequences and non-periodic ones. For the solution of a periodic finite sequence, we use finite Fourier series which in this book we refer to as discrete transformation. But to solve the non-periodic finite sequence, it is first necessary to transform it into a periodic sequence which can be done by adding some new equations to the system and then deal with it as a periodic finite sequence. Last section concerned with the solutions of the infinite sequence by using the method of Euler's scheme.