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

`(b)/(a)=(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.