  In this note, we establish a new closed formula for the solution of
homogeneous second-order linear difference equations with constant coefficients
by using matrix theory. This, in turn, gives new closed formulas concerning all
sequences of this type such as the Fibonacci and Lucas sequences. As
applications; we show that Binet's formula, in this case, is valid for negative
integers as well. Finally, we find new summation formulas relating the elements
of such sequences.
