Question

The sum of three distinct positive real numbers in geometric progression is $x$ times the middle term, then the value of $x$ lies in the set

• A. $(0,1)$
• B. $(-1,0)\cup (1,2)$
• C. $(-\infty ,-1)\cup (3,\infty )$
• D. $(3,\infty )$

Answer 1

The correct option is D $(3,\infty )$

Let the three numbers in G.P. are $\frac{a}{r},a,ar$
$\therefore \frac{a}{r}+a+ar=xa\Rightarrow \frac{a}{r}+ar=xa-a\Rightarrow \frac{1}{r}+r=x-1\Rightarrow x-1>2(\because r>0)\Rightarrow x>3$