The 3rd and 7th term of a GP are 24 and 8/27 respectively . Calculate the positive value of the common ratio

The $n$-th term of a Geometric Progression is given by $a_n = a \cdot r^{n-1}$, where $a$ is the first term and $r$ is the common ratio.

The 3rd term ($a_3$) is 24:

The 7th term ($a_7$) is $\frac{8}{27}$:

To find $r$, take the fourth root of both sides:

Since we are asked for the positive value of the common ratio:

The positive value of the common ratio is $\frac{1}{3}$.