$\backslash$table$[[$sequence$,\backslash$table$[[$geometric$?],[($yes or no$)]],\backslash$table$[[$common ratio?$],[("r""$ or n$/$a$)]],\backslash$table$[[$convergent$],[$or$],[$divergent$?]],$justification$],[a_n=\frac{5^{n1}}{2^{2n-1}},,,,],[,,,,],[a_n=(\frac{n}{4}{)}^n,,,,],[\frac{3}{5},-\frac{6}{25},\frac{12}{125},-\frac{24}{625},$dots,,,,$]]$Wed