For a $G$.$P$.,if $S_n = \frac{4^n - 3^n}{3^n}$,then $t_2 = ........$

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,then the value of $a(b - c)\log a + b(c - a)\log b + c(a - b)\log c$ is:

If $1+\cos x+\cos ^2 x+\cos ^3 x+\ldots \text{ to } \infty = 4+2 \sqrt{3}$,then $x=$

If $y = x - x^2 + x^3 - x^4 + \dots \infty$,then the value of $x$ will be

If $x$ is added to each of the numbers $3, 9, 21$ so that the resulting numbers are in $G.P.$,then the value of $x$ is:

If $a, b, c, d$ and $p$ are different real numbers such that $(a^{2}+b^{2}+c^{2}) p^{2}-2(ab+bc+cd) p+(b^{2}+c^{2}+d^{2}) \leq 0$,then show that $a, b, c$ and $d$ are in $G.P.$