Let $S_1, S_2, \dots, S_{101}$ be the consecutive terms of an $A.P$. If $\frac{1}{S_1 S_2} + \frac{1}{S_2 S_3} + \dots + \frac{1}{S_{100} S_{101}} = \frac{1}{6}$ and $S_1 + S_{101} = 50$,then $|S_1 - S_{101}|$ is equal to

If the sides of a right-angled triangle are in an arithmetic progression,then they are in the ratio of.........

Statement-$I$: If the ratio of the sum of $n$ terms of two arithmetic progressions is $(7n + 1) : (4n + 17)$,then the ratio of their $n^{th}$ terms is $7 : 4$.
Statement-$II$: If $S_n = an^2 + bn + c$,then $T_n = S_n - S_{n-1}$.

$A$ 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?

Let $\frac{1}{x_1}, \frac{1}{x_2}, \frac{1}{x_3}, \dots, \frac{1}{x_n}$ ($x_i \neq 0$ for $i = 1, 2, \dots, n$) be in $A.P.$ such that $x_1 = 4$ and $x_{21} = 20$. If $n$ is the least positive integer for which $x_n > 50$,then $\sum_{i=1}^n \left( \frac{1}{x_i} \right)$ is equal to:

Suppose we have an arithmetic progression $a_1, a_2, \ldots, a_n, \ldots$ with $a_1 = 1$ and $a_2 - a_1 = 5$. The median of the finite sequence $a_1, a_2, \ldots, a_k$,where $a_k \leq 2021$ and $a_{k+1} > 2021$,is