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

The ${n^{th}}$ term of the series $3 \cdot 8 + 6 \cdot 11 + 9 \cdot 14 + 12 \cdot 17 + \dots$ will be

Let the sequence $a_{n}$ be defined as follows:
$a_{1} = 1, a_{n} = a_{n-1} + 2$ for $n \ge 2$
Find the first five terms and write the corresponding series.

If $a, b, c$ are in $A.P.$,then $3^a, 3^b, 3^c$ shall be in

If the sum of the first $10$ terms of an arithmetic progression is $4$ times the sum of its first $5$ terms,then the ratio of its first term to the common difference is......

Let $a_1, a_2, \ldots, a_n$ be in an $A$.$P$. If $a_5 = 2a_3$ and $a_{11} = 18$,then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}} + \frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}} + \ldots + \frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to $..........$.