  In this paper, authors construct a new type of sequence which is named an
extra-super increasing sequence, and give the definitions of the minimal super
increasing sequence {a[0], a[1], ..., a[n]} and minimal extra-super increasing
sequence {z[0], z[1], ..., z[n]}. Find that there always exists a fit n which
makes (z[n] / z[n-1] - a[n] / a[n-1])= PHI, where PHI is the golden ratio
conjugate with a finite precision in the range of computer expression. Further,
derive the formula radic(5) = 2(z[n] / z[n-1] - a[n] / a[n-1]) + 1, where n
corresponds to the demanded precision. Experiments demonstrate that the
approach to radic(5) through a term ratio difference is more smooth and
expeditious than through a Taylor power series, and convince the authors that
lim(n to infinity) (z[n] / z[n-1] - a[n] / a[n-1]) = PHI holds.
