Consider an $A$.$P$.: $a_1, a_2, \dots, a_n$, with $a_1 > 0$. If $a_2 - a_1 = -\frac{3}{4}$, $a_n = \frac{1}{4} a_1$, and $\sum_{i=1}^n a_i = \frac{525}{2}$, then $\sum_{i=1}^{17} a_i$ is equal to:

The minimum value of ${\left( {\frac{3}{a} - 1} \right)^2} + {\left( {\frac{a}{b} - 1} \right)^2} + {\left( {\frac{b}{c} - 1} \right)^2} + {\left( {3c - 1} \right)^2}$ where $0 < a, b, c \leqslant 9$,is $p - q\sqrt{r}$; $p, q, r \in I$ and $q, r$ are coprime,then $(p + q + r)$ is equal to

Find the sum to $n$ terms of the $A.P.$ whose $k^{\text{th}}$ term is $5k+1$.

The sum of the first $n$ natural numbers is

If the first term of an arithmetic progression is $2$ and the common difference is $4$,then the sum of its first $40$ terms is........

If the $n^{th}$ term of an $A.P.$ is $(2n - 1)$,then the sum of its first $n$ terms is