Is it possible to solve for x and y?

Question

Given that

$3, \frac{3}{x}, \frac{3x}{y}, {7y}$

Are terms of an Arithmetic Progression. Is it possible to solve for $x$ and $y$? I tried the usual way getting 2 equations for the first three and last three terms but unable to solve them. Also I tried by taking various values and somehow luckily got a solution $x= \frac{6}{7}; y=\frac{9}{14}$

Is this the only solution?

Answer 1

Use the Arithmetic Progression Formula

$a_n=a_1+(n-1)d$

Hence $\frac{3}{x}=3+d\to d=\frac{3}{x}-3$

Then $\frac{3x}{y}=3+2d=3(\frac{3}{x}-3)$

and so forth.