Q.Write the molecular formula of the first six members of homologous series of nitro alkanes.

A homologous series is a run of organic compounds that all share one characteristic functional group, and whose successive members differ from each other in molecular formula by exactly one $CH_2$ unit -- for example the alkanes (methane $CH_4$, ethane $C_2H_6$, propane $C_3H_8$...) or the alcohols (methanol $CH_3OH$, ethanol $C_2H_5OH$, propanol $C_3H_7OH$...).

Because every member of a series shares the same functional group and the same $CH_2$-unit spacing, the entire series can be captured by ONE general formula: alkanes are $C_nH_{2n+2}$, alkenes are $C_nH_{2n}$, alkynes are $C_nH_{2n-2}$ -- and since an alkadiene (a chain with two C=C double bonds) has the same degree of unsaturation as an alkyne (one C≡C triple bond, or two degrees of unsaturation total), alkadienes share the alkyne formula, $C_nH_{2n-2}$. This same general-formula logic extends class by class: an aliphatic monohydric alcohol is $C_nH_{2n+1}OH$ (one -OH on a saturated chain); aliphatic ketones are $C_nH_{2n}O$ (one C=O on a saturated chain, needing at least 3 carbons since the carbonyl carbon needs two carbon substituents); aliphatic amines are $C_nH_{2n+3}N$ (one -NH2, or a substituted nitrogen, on a saturated chain); nitroalkanes are $C_nH_{2n+1}NO_2$ for the first six members: $CH_3NO_2$ (nitromethane), $C_2H_5NO_2$ (nitroethane), $C_3H_7NO_2$ (nitropropane), $C_4H_9NO_2$ (nitrobutane), $C_5H_{11}NO_2$ (nitropentane), $C_6H_{13}NO_2$ (nitrohexane). …