Let $\omega$ be a complex number such that $\omega^7 = 1$ and $\omega \ne 1.$ Compute \[\omega^{16} + \omega^{18} + \omega^{20} + \dots + \omega^{54}.\]

Let w be a complex number such that w^7 = 1 and w does not = 1.
Compute w^16 + w^18 + w^20 + ... + w^54