Write the seventh term of the following $GP$: $21a, 84a^3, 336a^5, 1344a^7, \dots$

The sum to infinity of the following series $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \dots$ is:

If $1+(1-2^{2} \cdot 1)+(1-4^{2} \cdot 3)+(1-6^{2} \cdot 5)+\ldots+(1-20^{2} \cdot 19) = \alpha - 220 \beta$,then an ordered pair $(\alpha, \beta)$ is equal to

If the sum of first $n$ terms of an $A.P.$ is $cn(n - 1)$,where $c \neq 0$,then the sum of the squares of these terms is

The sum of the series $3.6 + 4.7 + 5.8 + \dots$ up to $(n - 2)$ terms is:

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