when AR is falling why MR falls at a faster rate than AR?​

Dear student, 
Under imperfect competition in order to sell more the firm must lower the price. This suggests that both AR and MR curves are downward sloping. Mathematically, it is only when the MR falls at a faster rate that the AR would fall. 

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AR is falling only in the case of monopoly and monopolistic competition. This is because a monopoly firm can sell any quantity of output at a higher price. But, it can sell more by lowering its price. This is the reason why AR is falling. When AR is falling, MR falls faster than AR because a given fall in MR is average out in the estimation of AR.
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