Question

find "x" so that 2+x,2+2x,2+4x are in GP

Answer 1

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Answer 2

Answer: The value of x is zero.

Step-by-step explanation:  The given geometric progression (G.P.) is  $2+x,~2+2x~2+4x.$

We know that in a geometric progression, every term is equal to the product of the previous term and the common ratio, i.e., we can say

second term : first term = third term : second term.

According to the given G.P., we can write

$(2+2x) : (2+x) = (2+4x) : (2+2x)\\\\\Rightarrow \dfrac{2+2x}{2+x}=\dfrac{2+4x}{2+2x}\\\\\Rightarrow (2+2x)^{2}=(2+x)(2+4x)\\\\ \Rightarrow 4(1+x)^{2}=2(2+x)(1+2x)\\\\\Rightarrow 2(1+x)^{2} =(2+x)(1+2x)\\\\\Rightarrow 2(1+2x+x^{2}  )=2+4x+x+2x^{2}  \\\\\Rightarrow 2+4x+2x^{2} =2+5x+2x^{2} \\\\\Rightarrow x=0.$

Thus, the value of $x$ is 0.