As the frequency of an AC circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?

Reactance of an inductor of inductance $L$is, $X_L=2\mathrm{\pi \nu L}$ where, $\nu$ is frequency of the AC circuit.

Reactance of a capacitor of capacitance C,   $X_C=\frac{1}{2\pi \nu C}$

On increasing frequency $\nu$, clearly $X_L$increases and $X_C$ decreases. 

For a L-C-R circuit, Impedance of the circuit  $Z=\sqrt{R^2+{(X_L-X_C)}^2}=\sqrt{R^2+{\left(2\mathrm{\pi \nu L}-\frac{1}{2\mathrm{\pi \nu C}}\right)}^2}$

As frequency ($\nu$) increases, Z decreases and at certain value of frequency known as resonant frequency (${\nu }_0$),  $X_L=X_C$, and impedance Z is minimum i.e., Z_min = R. When frequency increases beyond resonant frequency, Z increases again.

As current varies inversely with impedance, current increases with decreasing Z, at Z=Z_min, current is maximum, and after that current starts decreasing with increasing Z.

Hence the circuit is either L-C-R or L-C circuit.