Let $b_1, b_2,......, b_n$ be a geometric sequence such that $b_1 + b_2 = 1$ and $\sum\limits_{k = 1}^\infty {{b_k} = 2} $ Given that $b_2 < 0$ , then the value of $b_1$ is
$2 - \sqrt 2 $
$1 + \sqrt 2 $
$2 + \sqrt 2 $
$4 + \sqrt 2 $
Let $a_{1}, a_{2}, a_{3}, \ldots$ be a G.P. such that $a_{1}<0$; $a_{1}+a_{2}=4$ and $a_{3}+a_{4}=16 .$ If $\sum\limits_{i=1}^{9} a_{i}=4 \lambda,$ then $\lambda$ is equal to
If $G$ be the geometric mean of $x$ and $y$, then $\frac{1}{{{G^2} - {x^2}}} + \frac{1}{{{G^2} - {y^2}}} = $
If $a,\;b,\;c$ are in $A.P.$, then ${10^{ax + 10}},\;{10^{bx + 10}},\;{10^{cx + 10}}$ will be in
$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $
The $G.M.$ of roots of the equation ${x^2} - 18x + 9 = 0$ is