If the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ are in arithmetic progression,then $k$ is equal to

The number of $5$-tuples $(a, b, c, d, e)$ of positive integers such that:
$I.$ $a, b, c, d, e$ are the measures of angles of a convex pentagon in degrees.
$II.$ $a \leq b \leq c \leq d \leq e$.
$III.$ $a, b, c, d, e$ are in an arithmetic progression.

$A$ man starts repaying a loan with a first installment of $Rs. 100$. If he increases the installment by $Rs. 5$ every month,what amount will he pay in the $30^{th}$ installment?

If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of the last and first term is $273$,then the numbers are

Let $a_n$ be the $n^{\text{th}}$ term of an $A.P.$ If $S_n = a_1 + a_2 + a_3 + \dots + a_n = 700$,$a_6 = 7$,and $S_7 = 7$,then $a_n$ is equal to:

If the sum of the first four terms of an $A.P.$ is $6$ and the sum of its first six terms is $4$,then the sum of its first twelve terms is