Compare terms of two progressions

Prove that the $(n+1{)}^{\text{th}}$ term of a G. P., of which the first term is $a$ and the third term $b$, is equal to the $(2n+1{)}^{\text{th}}$ term of a G. P. of which the first term is $a$ and the fifth term $b$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 7