  We theoretically study the energy and optical absorption spectra of
alternating twist multilayer graphene (ATMG) under a perpendicular electric
field. We obtain analytically the low-energy effective Hamiltonian of ATMG up
to pentalayer in the presence of the interlayer bias by means of first-order
degenerate-state perturbation theory, and present general rules for
constructing the effective Hamiltonian for an arbitrary number of layers. Our
analytical results agree to an excellent degree of accuracy with the numerical
calculations for twist angles $\theta \gtrsim 2.2^{\circ}$ that are larger than
the typical range of magic angles. We also calculate the optical conductivity
of ATMG and determine its characteristic optical spectrum, which is tunable by
the interlayer bias. When the interlayer potential difference is applied
between consecutive layers of ATMG, the Dirac cones at the two moir\'{e}
Brillouin zone corners $\bar{K}$ and $\bar{K}'$ acquire different Fermi
velocities, generally smaller than that of monolayer graphene, and the cones
split proportionally in energy resulting in a step-like feature in the optical
conductivity.
