For what values of x are the numbers frac{2}{ | vedclass

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(C) For three numbers $a, b, c$ to be in $G.P.$,the condition is $b^2 = ac$.
Here,$a = \frac{2}{7}$,$b = x$,and $c = -\frac{7}{2}$.
Substituting the

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$\pm 1$

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(C) For three numbers $a, b, c$ to be in $G.P.$,the condition is $b^2 = ac$.
Here,$a = \frac{2}{7}$,$b = x$,and $c = -\frac{7}{2}$.
Substituting these values into the condition:
$x^2 = \left(\frac{2}{7}ight) 	imes \left(-\frac{7}{2}ight)$
$x^2 = -1$
In the set of real numbers,the square of a number cannot be negative. Therefore,there are no real values of $x$ that satisfy this condition.
If the question intended for the sequence to be $\frac{2}{7}, x, \frac{7}{2}$ (where $c = \frac{7}{2}$),then $x^2 = \left(\frac{2}{7}ight) 	imes \left(\frac{7}{2}ight) = 1$,which gives $x = \pm 1$.
Given the options,it is highly probable that the intended sequence was $\frac{2}{7}, x, \frac{7}{2}$.

For what values of $x$ are the numbers $\frac{2}{7}, x, -\frac{7}{2}$ in $G.P.$?

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