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

a
n+12n+1
b
n(n+1)d2n+1
c
(n+2)d2n
d
(n-1)d2n+1

detailed solution

Correct option is B

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

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