If $a,\;b,\;c,\;d$ and $p$ are different real numbers such that $({a^2} + {b^2} + {c^2}){p^2} - 2(ab + bc + cd)p + ({b^2} + {c^2} + {d^2}) \le 0$, then $a,\;b,\;c,\;d$ are in
$A.P.$
$G.P.$
$H.P.$
$ab = cd$
If $x,\;y,\;z$ are in $G.P.$ and ${a^x} = {b^y} = {c^z}$, then
Find the sum of the following series up to n terms:
$6+.66+.666+\ldots$
If the roots of the cubic equation $a{x^3} + b{x^2} + cx + d = 0$ are in $G.P.$, then
The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is