Question

If 1, x, y is a geometric progression and x, y, 3 is an arithmetic
progression, then the value of (x + y) can be​

Answer 1

Answer:

it can be 0, 1, 10/9.

Answer 2

Answer:

The values can be $0,10/9$.

Step-by-step explanation:

It is given that $1, x, y$ is a geometric progression.

$x, y, 3$ is an arithmetic progression.

We need to evaluate the value of $x+y$.

From the geometric sequence,

$x/1=y/x$

$y=x^{2}$

From arithmetic sequence,

$y-x=3-y$

$2y=x+3$

$y=(x+3)/2$

Comparing both values, we get

$x^{2} =(x+3)/2$

$2x^{2} -x-3=0$

$(2x-3)(x+1)=0$

$x=2/3,-1$

For $x=2/3, y=4/9,x+y=10/9$

Similarly

For $x=-1,y=1,x+y=0$

The values can be $0,10/9$.

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