The $15^{th}$ term of the arithmetic progression $4 + 9 + 14 + 19 + \dots$ is......

If the sum of three numbers in an arithmetic sequence is $15$ and the sum of their squares is $83$,then the numbers are

Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$,then the value of $\frac{S_{4n}}{S_{2n}}$ is:

If $\sum_{r=1}^n(2r+1)=440$,then $n = \ldots$.

The first term of an $A.P.$ is $2$ and the common difference is $4$. The sum of its $40$ terms will be:

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$,then $8 \sigma^2$ is equal to