A body moves on a frictionless plane starting from rest. If S_n is distance moved between t=n-1 and t = n and S_n -1 is distance moved between t = n…

A body moves on a frictionless plane starting from rest. If $\displaystyle S_n$ is distance moved between $\displaystyle t=n-1$ and $\displaystyle \mathrm{t}=\mathrm{n}$ and $\displaystyle \mathrm{S}_{\mathrm{n}-1}$ is distance moved between $\displaystyle \mathrm{t}=\mathrm{n}-2$ and $\displaystyle \mathrm{t}=\mathrm{n}-1$, then the ratio $\displaystyle \frac{\mathrm{S}_{\mathrm{n}-1}}{\mathrm{~S}_{\mathrm{n}}}$ is $\displaystyle \left(1-\frac{2}{x}\right)$ for $\displaystyle \mathrm{n}=10$. The value of $\displaystyle x$ is $\displaystyle \_\_\_\_$.