Let the principal be ( P ).

Amount after 1 year: ( A_1 = P\bigl(1 + \dfrac{r}{100}\bigr) )

Amount after 2 years: ( A_2 = P\bigl(1 + \dfrac{r}{100}\bigr)^2 )

Amount after 3 years: ( A_3 = P\bigl(1 + \dfrac{r}{100}\bigr)^3 )

…

Amount after ( n ) years: ( A_n = P\bigl(1 + \dfrac{r}{100}\bigr)^n )

The sequence ( A_1, A_2, A_3, \ldots, A_n ) has common ratio [ \frac{A_{k+1}}{A_k} = 1 + \dfrac{r}{100} ] (constant).

Hence the amounts form a geometric progression.

Answer: Proved (common ratio ( 1 + \dfrac{r}{100} ))