If the first term of an $A.P.$ is $10$,the last term is $50$,and the sum of all the terms is $300$,then the number of terms is:

If $p$ times the $p^{th}$ term of an arithmetic progression is equal to $q$ times its $q^{th}$ term,then the $(p + q)^{th}$ term of this progression is........

If the sum of $n$ terms of the sequence $2, 5, 8, 11, \dots$ is $60100$,then $n = \dots$

If $a\left(\frac{1}{b}+\frac{1}{c}\right), b\left(\frac{1}{c}+\frac{1}{a}\right), c\left(\frac{1}{a}+\frac{1}{b}\right)$ are in $A.P.$,prove that $a, b, c$ are in $A.P.$

The sum of $n$ arithmetic means between $a$ and $b$ is:

Let $a_1, a_2, a_3, \dots$ be an $A.P.$ with $a_6 = 2$. Then the common difference of this $A.P.$,which maximizes the product $a_1 a_4 a_5$,is