If $a_n=\int_0^{\frac{\pi}{2}} \frac{\sin ^2 n x}{\sin x} d x$, then $a_2-a_1, a_3-a_2, a_4-a_3$ are in

• A

  Arithmetic progression
• B

  Geometric progression
• Correct answer
  C

  Harmonic progression
• D

  Arithmetico-geometric progression

Hence, the correct answer is option: 'C'.