No, Prasenjeet, we cannot lump alkanes, alkynes and alkenes into one "homologous" series.
The general formula for an alkane is CnH2n + 2 (n ≥ 1) in which the repeating unit is -CH2-
For 1-alkenes the general formula is CnH2n (n ≥ 2) for which the repeating unit is also -CH2-, but notice how the general formula differs from that of alkanes.
As a final example consider 1-alkynes for which the general formula is CnH2n − 2 (n ≥ 2).
Compounds form a homologous series as long as they have the same general formula. Thus methane, ethane, propane, butane etc. form one homologous series (the alkanes). Alkenes and alkynes form their own series.