  We give estimates for the first two moments of arithmetical sequences in
progressions. Instead of using the standard approximation, we work with a
generalization of Vaughan's major arcs approximation which is similar to that
appearing in earlier work of Browning and Heath-Brown on norm forms. We apply
our results to the sequence $\tau_k(n)$, and obtain unconditional results in a
wide range of moduli.
