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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$\pm 1$

Vedclass · Answer

(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 $G.P.$?

Similar Questions

If every term of a $G.P.$ with positive terms is the sum of its two previous terms,then the common ratio of the series is

The money invested in a company is compounded continuously. If ₹ $200$ invested today becomes ₹ $400$ in $6$ years, then at the end of $33$ years it will become ₹ (in $\sqrt{2}$)

The arithmetic mean of two numbers $b$ and $c$ is $a$,and $g_1$ and $g_2$ are two geometric means between them. If $g_1^3 + g_2^3 = kabc$,then $k = \dots$

Find the sum of the first $n$ terms and the sum of the first $5$ terms of the geometric series $1 + \frac{2}{3} + \frac{4}{9} + \dots$

If $n$ geometric means between $a$ and $b$ are $G_1, G_2, ..., G_n$ and a single geometric mean is $G$,then the true relation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module