Question

Find xif 4; 4+2×;4+4× are in Geometric sequences​

Answer 1

Given:

$4,4+2x,4+4x$ are in geometric sequences​.

To find:

The value of x.

Solution:

If a, b, c are in geometric sequences​, then

$\dfrac{b}{a}=\dfrac{c}{b}$

$b^2=ac$           ...(i)

It is given that $4,4+2x,4+4x$ are in geometric sequences​. By using (i), we get

$(4+2x)^2=(4)(4+4x)$

$4^2+2(4)(2x)+(2x)^2=(4)(4)+4(4x)$

$16+16x+4x^2=16+16x$

$4x^2=16+16x-16-16x$

On further simplification, we get

$4x^2=0$

$x^2=0$

$x=0$

Therefore, the value of x is 0.