Find $a, b$ and $c$ such that the following numbers are in $AP : a, 7, b, 23, c$.

For a given $A.P.$,$a=2$ and $d=3$. Then,$S_{30} = \dots$

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \ldots \ldots \ldots \ldots$

For an $A.P.$,the $6^{th}$ term is $19$ and the $17^{th}$ term is $41$. Find the $40^{th}$ term of the $A.P.$

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 2n - 1$. Then,the $10^{th}$ term of the $A.P.$ is.........

From natural numbers $1$ to $288,$ find the number $x$ such that the sum of all natural numbers smaller than $x$ is equal to the sum of all natural numbers greater than $x$ but less than or equal to $288.$