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I need to edit this code so the red dashed line can end up at R4 not R3 as in the following picture .

 documentclass[tikz,border=3.14mm]{standalone}

 usetikzlibrary{positioning,calc,arrows.meta}

begin{document}

begin{tikzpicture}[bullet/.style={draw,circle,minimum width=3mm,inner 

sep=0pt,

fill=cyan!50}]

node[bullet,label={[yshift=-2mm]below:$R_1$}] (R1){};

node[right=2cm of R1,bullet,label={[yshift=-2mm]below:$R_2$}] (R2){};

node[right=2cm of R2,yshift=6mm,bullet,label={[yshift=2mm]above:$R_3$}] (R3) 

 {};

node[right=2cm of R3,yshift=-6mm,bullet,label={[yshift=-2mm]below:$R_4$}] 

  (R4){};

  node[right=2cm of R4,bullet,label={[yshift=-2mm]below:$R_5$}] (R5){};

foreach X [evaluate=X as Y using {int(X+1)}] in {1,...,4}

{draw[thick,-latex,cyan!50] (RX) -- (RY);}





 draw[thick,red,{Circle}-latex,dashed] let p1=($(R2)-(R1)$), p2=($(R3)- 

(R2)$), 

n1={atan2(y1,x1)},n2={atan2(y2,x2)} in 

([yshift=1mm]R1.north) to[out=n1,in=180,looseness=0.5] 

([yshift=1mm]R2.north) to[out=0,in=n2-180,looseness=0.5] 

  ([yshift=1mm,xshift=-2mm]R3.north);



  end{tikzpicture}

      end{document}

You need to add some code for the red line:

draw[thick,red,{Circle}-latex,dashed] let p1=($(R2)-(R1)$), p2=($(R3)-(R2)$), p3=($(R4)-(R3)$),

n1={atan2(y1,x1)},n2={atan2(y2,x2)},n3={atan2(y3,x3)} in 

([yshift=1mm]R1.north) to[out=n1,in=180,looseness=0.5] 

([yshift=1mm]R2.north) to[out=0,in=n2-180,looseness=0.5] 

([yshift=1mm]R3.north) to[out=0,in=n3-180,looseness=0.5] 

([yshift=1mm,xshift=-2mm]R4.north);

With the complete MWE

documentclass[tikz,border=3.14mm]{standalone}



usetikzlibrary{positioning,calc,arrows.meta}





begin{document}

begin{tikzpicture}[bullet/.style={draw,circle,minimum width=3mm,inner sep=0pt,fill=cyan!50}]

node[bullet,label={[yshift=-2mm]below:$R_1$}] (R1){};

node[right=2cm of R1,bullet,label={[yshift=-2mm]below:$R_2$}] (R2){};

node[right=2cm of R2,yshift=6mm,bullet,label={[yshift=2mm]above:$R_3$}] (R3) 

 {};

node[right=2cm of R3,yshift=-6mm,bullet,label={[yshift=-2mm]below:$R_4$}] 

  (R4){};

  node[right=2cm of R4,bullet,label={[yshift=-2mm]below:$R_5$}] (R5){};

foreach X [evaluate=X as Y using {int(X+1)}] in {1,...,4}

{draw[thick,-latex,cyan!50] (RX) -- (RY);}





%draw[thick,red,{Circle}-latex,dashed] let p1=($(R2)-(R1)$), p2=($(R3)-(R2)$), 

draw[thick,red,{Circle}-latex,dashed] let p1=($(R2)-(R1)$), p2=($(R3)-(R2)$), p3=($(R4)-(R3)$),

n1={atan2(y1,x1)},n2={atan2(y2,x2)},n3={atan2(y3,x3)} in 

([yshift=1mm]R1.north) to[out=n1,in=180,looseness=0.5] 

([yshift=1mm]R2.north) to[out=0,in=n2-180,looseness=0.5] 

([yshift=1mm]R3.north) to[out=0,in=n3-180,looseness=0.5] 

([yshift=1mm,xshift=-2mm]R4.north);



end{tikzpicture}

end{document}

you get:

Instead of reconstructing the path of the red dotted arrow by clever calculations, you can use the preaction key which allows you to place the path in a temporary scope that you move vertically with transform canvas.

To make it look prettier, I rounded the angles with the rounded key rounded corners=5pt.

path[rounded corners=5pt,preaction={draw,red,thick,{Circle}-latex,

,transform canvas={yshift=3mm}}

] (R1.center)to(R2.center)to(R3.center)to(R4.center);

The result without the rounded corners:

documentclass[tikz,border=3.14mm]{standalone}

 usetikzlibrary{positioning,calc,arrows.meta}

begin{document}

begin{tikzpicture}[bullet/.style={draw,circle,minimum width=3mm,inner 

sep=0pt,

fill=cyan!50}]

node[bullet,label={[yshift=-2mm]below:$R_1$}] (R1){};

node[right=2cm of R1,bullet,label={[yshift=-2mm]below:$R_2$}] (R2){};

node[right=2cm of R2,yshift=6mm,bullet,label={[yshift=2mm]above:$R_3$}] (R3) 

 {};

node[right=2cm of R3,yshift=-6mm,bullet,label={[yshift=-2mm]below:$R_4$}] 

  (R4){};

  node[right=2cm of R4,bullet,label={[yshift=-2mm]below:$R_5$}] (R5){};

foreach X [evaluate=X as Y using {int(X+1)}] in {1,...,4}

{draw[thick,-latex,cyan!50] (RX) -- (RY);}



path[rounded corners=5pt,preaction={draw,red,thick,{Circle}-latex,

,transform canvas={yshift=3mm}}

] (R1.center)to(R2.center)to(R3.center)to(R4.center);

  end{tikzpicture}

      end{document}