If the $9^{th}$ term of an $A.P.$ is zero,then the ratio of its $29^{th}$ term to its $19^{th}$ term is:

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an $A.P.$ are $a, b,$ and $c$ respectively,find the value of $a(q-r) + b(r-p) + c(p-q)$.

What is the sum of all two-digit numbers which give a remainder of $4$ when divided by $6$?

Which term of the geometric sequence $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683}$?

Let $a_1, a_2, a_3, ..., a_n$ be in an $A.P.$ If $a_3 + a_7 + a_{11} + a_{15} = 72$,then the sum of its first $17$ terms is equal to:

Let ${a_n}$ be the ${n^{th}}$ term of the $G$.$P$. of positive numbers. Let $\sum\limits_{n = 1}^{100} {{a_{2n}}} = \alpha $ and $\sum\limits_{n = 1}^{100} {{a_{2n - 1}}} = \beta $,such that $\alpha \ne \beta $,then the common ratio is