  We present a general procedure for calculating the exact partition function
of an Ising model on a periodic chain in presence of magnetic field considering
both open and closed boundary conditions. Using same procedure on a
quasiperiodic (Fibonacci) chain we have established a recurrence relation among
partition functions of different Fibonacci generations from n-th to (n+6)-th.
In the large N limit we find $(2\tau + 1){F_{n+1}}={F_{n+2}}$; where $\tau$ is
the golden mean and $F_n$ stands for free energy/spin for the n-th generation.
We have also studied chemical potential in both cases.
