The correct answer is: B. The same number of carbon atoms are found, and similar functional groups are found.
A homogeneous series is a class of carbon compounds in which the same number of carbon atoms are found, and similar functional groups are found. This means that the compounds in a homogeneous series have the same molecular formula, but different structural formulas. For example, the alkanes are a homogeneous series of hydrocarbons with the general formula $C_n H_{2n+2}$. The first few members of the alkane series are methane ($CH_4$), ethane ($C_2 H_6$), propane ($C_3 H_8$), and butane ($C_4 H_{10}$).
The functional group is the part of a molecule that determines its chemical properties. The functional groups in the alkane series are all alkyl groups, which are groups of carbon and hydrogen atoms that are attached to a carbon atom. The alkyl groups in the alkane series are all the same, which is why the compounds in the alkane series have similar chemical properties.
The other options are incorrect because they do not describe a homogeneous series. Option A is incorrect because it states that different numbers of carbon atoms are found in a homogeneous series. Option C is incorrect because it states that different numbers of carbon atoms are found, but similar functional groups are found. Option D is incorrect because it states that the same number of carbon atoms are found, but different functional groups are found.