proof verification - Mathematical Induction Basis Step Not Equal

I am to prove the following statement using mathematical induction for all positive integers:
$$
1 - 2 + 2^2 - 2^3 +\dots+(-1)^n 2^n =
\frac{2^n\cdot2^1\cdot(-1)^n+1}{3}.
$$
However, for the basis step, I am getting $-2$ for the left side and $-1$ for the right side, which are obviously not equal. The assignment indicates that the statement is true though, so I am missing something or could this be a typo in the statement?