We study the thermopower and the electrical conductance of a ballistic InAs nano-wire in the presence of Rashba spin-orbit interaction and an in-plane magnetic field. We consider a parabolic confinement in the direction perpendicularto the wire axis.The quantum confi- nement gives rise to discrete energy subbands that may contain local extrema due to the combined effect of Rashba interaction and the magnetic field. Such extremawill influence the behaviour of the conductance and thermopower of the nano-wire. We found that the local minimum causes the conductance to increase in step of e2/h, which is doubled for certain direction of the magnetic field due to degeneracy. Howeverm the local maximum causes the conductance to decrease in step of e2/h. Our calculations show that the thermopower, in units of kB ln2/e, consists of positive peaks for local minima and maxima respectively in the dispersion relation. In the absence of intersubband coupling the peaks show pattern repetition and may also show degeneracy corresponding to that of the conductance. The repitition in the thermopower disappears if the intersubband coupling is taken into account. Therfore the pattern repititionofthe thermopower peaks istiedwith theexistence of intersubband coupling. Finally we comparedour single-particle formula to the standard Mott's equation which represents a good approximation tothe thermopower at low temperatures. The comparaison shows excellent agreement that validates our reults.