1. Tardigrade
  2. Question
  3. Mathematics
  4. If a, b and c be three distinct real numbers in G. P. and a + b + c = xb, then x cannot be :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If a, b and c be three distinct real numbers in $G. P$. and $a + b + c = xb$, then $x$ cannot be :

JEE MainJEE Main 2019Sequences and Series

Solution:

$\frac{b}{r} , b, br \to G.P. \; \; \left(\left|r\right| \ne1\right) $
given $a + b + c = xb$
$\Rightarrow $ $b/r + b + br = xb$
$\Rightarrow $ $b = 0$ (not possible)
or $1+ r + \frac{1}{r} =x \Rightarrow x - 1 = r + \frac{1}{r}$
$ \Rightarrow x-1 >2 $ or $ x-1 < - 2 $
$ \Rightarrow x>3$ or $ x<-1 $
So $x$ can't be $'2'$