Write down the $20^{th}$ term of the $G.P. 1, -1, 1, -1, \ldots$

The product of $n$ positive numbers is unity. Their sum is

The sum of an infinite number of terms in a $G.P.$ is $20$ and the sum of their squares is $100$. The common ratio of the $G.P.$ is:

If ${a_1}, {a_2}, {a_3}, \dots, {a_n}$ are in $H.P.$,then ${a_1}{a_2} + {a_2}{a_3} + \dots + {a_{n-1}}{a_n}$ is equal to:

The difference between the fourth term and the first term of a Geometric Progression is $52.$ If the sum of its first three terms is $26,$ then the sum of the first six terms of the progression is

If $\sum\limits_{i = 1}^{20} {\left( {\frac{{{}^{20}{C_{i - 1}}}}{{{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \right)} ^3 = \frac{k}{21}$,then $k$ equals