The mean deviation of the series a, a+d, a+2d, ...., a+(2n-1)d, a+2nd about the mean is

The mean of the given series is a+nd. ∴      Mean deviation about mean        =1(2n+1)∑r=02n |(a+rd)−(a+nd)|=d2n+1∑r=02n |r−n|=2d2n+1∑r=1n r=2d2n+1×n(n+1)2=n(n+1)d2n+1