Sum of partial sums of GP

If $S_n$ denote the sum of $n$ terms of a G. P. whose first term is $a$, and common ratio $r$, find the sum of $S_1$, $S_3$, $S_5$, ... $S_{2n-1}$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 21