If $4^{\text{th}}$,$10^{\text{th}}$,and $16^{\text{th}}$ terms of a $G$.$P$. are $x, y$,and $z$ respectively,then

If the sum of three terms of a Geometric Progression $(GP)$ is $19$ and their product is $216$,then the common ratio of this $GP$ is:

Find the $12^{\text{th}}$ term of a $G.P.$ whose $8^{\text{th}}$ term is $192$ and the common ratio is $2$.

Let $729, 81, 9, 1, \dots$ be a sequence and $P_{n}$ denote the product of the first $n$ terms of this sequence. If $2\sum_{n=1}^{40}(P_{n})^{\frac{1}{n}}=\frac{3^{\alpha}-1}{3^{\beta}}$ and $\gcd(\alpha,\beta)=1$, then $\alpha+\beta$ is equal to

Find four numbers forming a geometric progression in which the third term is greater than the first term by $9,$ and the second term is greater than the $4^{\text{th}}$ term by $18.$

In a geometric progression consisting of positive terms,each term equals the sum of the next two terms. Then the common ratio of its progression is equal to: