42
43
51
52
Answer is Right!
Answer is Wrong!
The answer is $\boxed{\text{52}}$.
The sequence is generated by adding $1$ to the first number, then adding $4$ to the second number, then repeating the pattern. So the next number in the sequence is $34 + 4 = \boxed{\text{52}}$.
Option A, $42$, is incorrect because it is not the next number in the sequence.
Option B, $43$, is incorrect because it is not the next number in the sequence.
Option C, $51$, is incorrect because it is not the next number in the sequence.
Option D, $52$, is correct because it is the next number in the sequence.