Question Number 154252 by EDWIN88 last updated on 16/Sep/21
$$\:\:{The}\:\left\{{x}_{{n}} \right\}\:{sequence}\:{is}\:{specified} \\ $$$$\:{by}\:{the}\:{conditions}\: \\ $$$$\:\:\begin{cases}{{x}_{\mathrm{1}} =\mathrm{1982}}\\{{x}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{4}−{x}_{{n}} },{n}\geqslant\mathrm{0}}\end{cases} \\ $$$$\:{find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{x}_{{n}} . \\ $$