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# For what value of $x$ the numbers $-\large\frac{2}{7},$$x,-\large\frac{7}{2} are in G.P.? \begin{array}{1 1} \pm 1 \\ \pm \frac{1}{2} \\ \pm \frac{1}{7} \\ \pm 2 \end{array} Can you answer this question? ## 1 Answer 0 votes Toolbox: • If x,y,z are in G.P. then common ratio r=\large\frac{y}{x}=\frac{z}{y} Given that -\large\frac{2}{7},$$x,-\large\frac{7}{2}$ are in G.P.
If $x,y,z$ are in G.P. then the common ratio $r= \large\frac{y}{x}=\frac{z}{y}$
$\Rightarrow\:\large\frac{x}{-2/7}=\frac{-7/2}{x}$
$\Rightarrow\:x^2=-\large\frac{7}{2}\times-\frac{2}{7}$
$\Rightarrow\:\:x^2=1$ or $x=\pm1$