If the mean deviation of the numbers 1, 1+d, 1+2d,...,1+100d from their mean is 255, then d is equal to

Let X denote the mean of the given numbers.Then,  X¯=1+(1+d)+(1+2d)+…+(1+100d)101⇒ X¯=1012{1+(1+100d))101=1+50d∴    Mean deviation =1101∑r=0100 |(1+rd)−(1+50d)|⇒   Mean deviation =1101∑r=0100 |r−50|⇒  Mean deviation =d101×2∑r=150r⇒  Mean deviation =2d101×50×512=50×51101d.It is given that the mean deviation is 255.∴ 255=50×51101d⇒d=10.1