Summary

Mathematica 11.0 code

sampling = Table[E^j, {j, -4, 2, 0.015}](*Table[10^j,{j,-2,0.7,0.01}]*);
p1 = Table[
   Show[
    ListPlot[Table[{x, Sin[2 \[Pi] x]}, {x, 0, 10, 1/50}], Joined -> True, DataRange -> {0, 10}, PlotStyle -> {Thick, Black}],
    ListPlot[Table[{x, Sin[2 \[Pi] x]}, {x, 0, 20, j}], Joined -> False, DataRange -> {0, 10}, PlotStyle -> {Red, PointSize[0.015]}],
    ListPlot[Table[{x, Sin[2 \[Pi] x]}, {x, 0, 20, j}], Joined -> True, DataRange -> {0, 10}, PlotStyle -> {Red}]
    , Axes -> False
    ]
   , {j, sampling}];
ListAnimate[p1]

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