  The large separations between the oscillation frequencies of solar-like stars
are measures of stellar mean density. The separations have been thought to be
mostly constant in the observed range of frequencies. However, detailed
investigation shows that they are not constant, and their variations are not
random but have very strong diagnostic potential for our understanding of
stellar structure and evolution. In this regard, frequencies of the minimum
large separation are very useful tools. From these frequencies, in addition to
the large separation and frequency of maximum amplitude, Y\i ld\i z et al.
recently have developed new methods to find almost all the fundamental stellar
properties. In the present study, we aim to find metallicity and helium
abundances from the frequencies, and generalize the relations given by Y\i ld\i
z et al. for a wider stellar mass range and arbitrary metallicity ($Z$) and
helium abundance ($Y$). We show that the effect of metallicity is {
significant} for most of the fundamental parameters. For stellar mass, for
example, the expression must be multiplied by $(Z/Z_{\sun})^{0.12}$. For
arbitrary helium abundance, $ M \propto (Y/Y_{\sun})^{0.25} $. Methods for
determination of $Z$ and $Y$ from pure asteroseismic quantities are based on
amplitudes (differences between maximum and minimum values of \Dnu) in the
oscillatory component in the spacing of oscillation frequencies. Additionally,
we demonstrate that the difference between the first maximum and the second
minimum is very sensitive to $Z$. It also depends on $\nu_{\rm min1}/\nu_{\rm
max}$ and small separation between the frequencies. Such a dependence leads us
to develop a method to find $Z$ (and $Y$) from oscillation frequencies. The
maximum difference between the estimated and model $Z$ values is about 14 per
cent. It is 10 per cent for $Y$.
