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satela [25.4K]
3 years ago
10

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

Mathematics
1 answer:
Ray Of Light [21]3 years ago
7 0

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.

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