If an=∫0π/2 sin2⁡nxsin⁡xdx then a2−a1,a3−a2,a4−a3 are in

n>1,an−an−1=∫0π/2 sin2⁡nx−sin2⁡(n−1)xsin⁡xdx=∫0π/2 sin⁡(2n−1)xsin⁡xsin⁡xdx=∫0π/2 sin⁡(2n−1)xdx=−cos⁡(2n−1)x2n−10π/2=12n−1which is a Harmonic Progression.