Manipulate[

Grid[ { { "Function Values: ((Subscript[a, n]), f((Subscript[a, n])))" , "Function Outputs: (n, f((Subscript[a, n])))" },

 { data=List[Transpose[{Table[ Sequence1[n][[sss]], {n, 1,t}], Table[ Function1[Sequence1[n][[sss]]][[hhh]], {n, 1, t}]}]]; 
ListPlot[data, PlotRange->{{-.5, .5}, {.5, 2}}, AspectRatio->1/1, ImageSize->Full], 

ListPlot[Table[Function1[Sequence1[n][[sss]]][[hhh]], {n, 1, t}],PlotRange->Automatic, ImageSize->Full]},

{ "Close-Up: ((Subscript[a, n]), f((Subscript[a, n])))" , "Tabular Values" }, 

{ data=List[Transpose[{Table[ Sequence1[n][[sss]], {n, 1,t}], Table[ Function1[Sequence1[n][[sss]]][[hhh]], {n, 1, t}]}]]; 
ListPlot[data, PlotRange->{{-.2, .2}, {.8, 1.6}}, AspectRatio->1/1, ImageSize->Full]  ,
 If[ t<6,TableForm[ Transpose[ {Range[1, t], Table[ Sequence1[n][[sss]], {n, 1, t} ], Table[N[Function1[Sequence1[n][[sss]]], 5][[hhh]], {n, 1, t}]}], TableHeadings->{ None, { "n", "(Subscript[a, n])", " f((Subscript[a, n]))"}},TableSpacing->{3, 6}], TableForm[Transpose[ {Range[t-5, t], Table[Sequence1[n][[sss]], {n, t-5, t} ], Table[N[Function1[Sequence1[n][[sss]]], 5][[hhh]], {n, t-5, t}]}], TableHeadings->{ None, { "n", "(Subscript[a, n])", " f((Subscript[a, n]))"}},TableSpacing->{3, 6}]]}},

ItemSize-> {{Scaled[.5], Scaled[.5]}},Frame-> All, Spacings -> {2, 2}],

{{sss, 4, "sequence"}, { 1->TraditionalForm[ 1 / n] ,2->TraditionalForm[ (-1)^n / n  ], 3->TraditionalForm[ 1 / n^2 ], 4->TraditionalForm[ (-1)^n / n^2], 5-> TraditionalForm[ 1 / Sqrt[n] ], 6->TraditionalForm[ (-1)^n / Sqrt[ n ]]}, SetterBar}, {{hhh, 3, "f(x)="}, {1->TraditionalForm[( x - 11/10 )^2 ], 2->TraditionalForm[ 3/2-x^2 ],3->TraditionalForm[ 3^x ]}, SetterBar},{{t, 1, "n"}, 1, 100,1},

Initialization :> ( Sequence1[n_]:={ 1 / n, (-1)^n / n, 1 / n^2,(-1)^n / n^2, 1 / Sqrt[n], (-1)^n / Sqrt[ n ] };
Function1[x_]:={ ( x - (11/10) )^2, 3/2 - x^2, 3^x })]