The answer is $\boxed{106}$.
The sequence is $10, 14, 26, 42, 70, 106$. The sequence is generated by adding the previous two numbers in the sequence. For example, $42 = 26 + 16$ and $70 = 42 + 28$.
Option A, $100$, is incorrect because it is not the sum of the previous two numbers in the sequence.
Option B, $102$, is incorrect because it is not the sum of the previous two numbers in the sequence.
Option C, $106$, is correct because it is the sum of the previous two numbers in the sequence.
Option D, $114$, is incorrect because it is not the sum of the previous two numbers in the sequence.