Question

If $b_1, b_2, b_3\left(b_1>0\right)$ are three successive terms of a G.P. with common ratio $r$, then value of $r$ for which the inequality $b_3>4 b_2-3 b_1$, holds is given by

• A. $r \geq 3$
• B. $1 < r < 2$
• C. $r>3$
• D. $r \in(0,1)$

Answer 1

Answer: (C)

$b_1, b_2, b_3$ are in G.P.
$\therefore b_3>4 b_2-3 b_1 $
$\Rightarrow r^2>4 r-3$
$\Rightarrow r^2-4 r+3>0$
$\Rightarrow (r-1)(r-3) >0 $
So $ 0< r< 1$ and $r>3$