In a series combination of three capacitors with capacitances $C$, $2C$, and $3C$ connected to a battery, what is the charge $Q$ on the first capacitor if the voltage across the first capacitor is $\Delta V_1$? Express $Q$ in terms of $C$ and $\Delta V_1$.
For the first capacitor, the charge and voltage are related by $Q = C\,\Delta V_1$. Since the first capacitor has capacitance $C$, the charge on it is $Q = C\Delta V_1$.
What the question is really asking
You are not being asked to use the whole series network yet. You only need the basic charge-voltage-capacitance relationship for the first capacitor.
Using the capacitor definition on capacitor 1
For any capacitor, $$Q = C\,\Delta V.$$
Here, capacitor 1 has capacitance $C$ and the voltage across it is given as $\Delta V_1$. Substituting: $$Q = C\,\Delta V_1.$$
Quick check
Units match: $C$ (farads) times $\Delta V_1$ (volts) gives coulombs, so the expression is consistent.
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