Sum of geometric series equality

The sum of $2n$ terms of a G. P. whose first term is $a$ and common ratio $r$ is equal to the sum of $n$ of a G. P. whose first term is $b$ and common ratio $r^2$. Prove that $b$ is equal to the sum of the first two terms of the first series.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 8