Answer: C (\(\text{C}_n\text{H}_{2n}\)). Alkenes are unsaturated hydrocarbons containing one carbon–carbon double bond, C=C. The general formula for the alkene homologous series is \(\text{C}_n\text{H}_{2n}\); for example ethene is C₂H₄ (n = 2) and propene is C₃H₆ (n = 3).
The other formulae do not fit the alkenes. Option D, \(\text{C}_n\text{H}_{2n+2}\), is the general formula for the saturated alkanes, which have two more hydrogen atoms than the alkene with the same number of carbons. Option B, \(\text{C}_n\text{H}_{2n-2}\), corresponds to a more unsaturated series (alkynes or dienes), not the alkenes. Option A, \(\text{C}_n\text{H}_{n+2}\), does not match any real hydrocarbon series.
Because the C=C double bond means an alkene has two fewer hydrogen atoms than the corresponding alkane, the general formula is \(\text{C}_n\text{H}_{2n}\) — answer C.
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