Sequence and Series

Concept:In a finite geometric progression, the product of two terms equidistant from the ends equals the product of the first and last term.Explanation:Let the G.P. be $a, ar, ar^2, \dots, ar^{n-1}$ where $a$ is the first term and $r$ the common ratio.The $k$-th term from the beginning is $ar^{k-1}$.The $k$-th term from the end is $ar^{n-k}$ (since the last term is $ar^{n-1}$).Their product is $(ar^{k-1})(ar^{n-k}) = a^2 r^{n-1}$.The product of first term $a$ and last term $ar^{n-1}$ is $a \cdot ar^{n-1} = a^2 r^{n-1}$.Thus, the products are equal. The statement is true.Answer:True