Capacitor and Resistance in a Series Circuit: Effects on Ammeter Reading?

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Peter G.
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There is a series circuit with a battery, resistor, capacitor and ammeter and a switch.
The question asks me what will happen to the ammeter reading when the switch is closed and why:

Well, I know that a capacitor charges up. What I am thinking is that as it charges up, it's resistance increases and therefore, the ammeter reading gradually decreases. Is that correct?
 
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As the capacitor charges the potential in the capacitor increases until it matches that of the source. You are quite right in saying that the current gradually decreaes.