Step 1: Start from the definition of AR:
$AR = \dfrac{TR}{Q} = \dfrac{P \times Q}{Q} = P$, so the AR curve is literally the same line as the price the monopolist charges at each quantity.
Step 2: Recall the monopolist's demand curve:
Because a monopolist is the only seller, the market demand curve IS the firm's demand curve, and by the law of demand it slopes downward.
Step 3: Combine the two facts:
Since AR = P and the firm's own demand curve (P against Q) is downward sloping, AR must also be downward sloping.
Final Answer:
Option C, downward sloping.