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 roots of the equation $x^3 - 12x^2 + 39x - 28 = 0$ are in $A.P.$,then their common difference will be

If the sum of $n$ terms of an arithmetic progression is $3n^2 + 5n$ and $t_n = 164$,then $n = \dots$

If $p(\frac{1}{q}+\frac{1}{r}), q(\frac{1}{r}+\frac{1}{p}), r(\frac{1}{p}+\frac{1}{q})$ are in $AP$,then $p, q, r$:

Let $S_n$ be the sum of the first $n$ terms of an arithmetic progression $3, 7, 11, \ldots$. If $40 < \left(\frac{6}{n(n+1)} \sum_{k=1}^{n} S_{k}\right) < 42$,then $n$ equals

The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is $10$,the number of such triangles is