The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is

For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,

Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd. 

Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer

Let $a_n$ be a sequence such that $a_1 = 5$ and $a_{n+1} = a_n + (n -2)$ for all $n \in N$, then $a_{51}$ is

The sequence $\frac{5}{{\sqrt 7 }}$, $\frac{6}{{\sqrt 7 }}$, $\sqrt 7 $, ....... is

Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$