The sum of the common terms of the following three arithmetic progressions.

$3,7,11,15,……………….,399$

$2,5,8,11,…………,359$ and

$2,7,12,17,………..,197$, is equal to $…………….$.

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 $\frac{1}{{{x_1}}},\frac{1}{{{x_2}}},\frac{1}{{{x_3}}},…..,$  $({x_i} \ne \,0\,for\,\,i\, = 1,2,….,n)$  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\limits_{i = 1}^n {\left( {\frac{1}{{{x_i}}}} \right)} $  is equal to.

Three number are in $A.P.$ such that their sum is $18$ and sum of their squares is $158$. The greatest number among them is

If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is