\pgfmathparse{1} \let\r\pgfmathresult;


\pgfmathparse{0.75} \let\dx\pgfmathresult;
\pgfmathparse{1.5} \let\dy\pgfmathresult;
\pgfmathparse{2} \let\k\pgfmathresult;

%Convex parameters for drawing lines
\pgfmathparse{1.75} \let\t\pgfmathresult;
\pgfmathparse{1-\t} \let\tt\pgfmathresult;

%Translation for point titles
\coordinate (Delta) at (0.035,-0.35);

\coordinate (V1) at (0.75,0.75);
\coordinate (V2) at (-0.75,0.75);



%Define nodes
\coordinate (A1) at ( 0,0);
\coordinate (A2) at ($(A1)+    (\dx,0)$);
\coordinate (Ak) at ($(A1)+ \k*(\dx,0)$);



\draw [] 
   ($\t*(A1)+\tt*(Ak)$)
   node[left] {$r_1$}
   --
   ($\tt*(A1)+\t*(Ak)$);

\coordinate (AA) at ($(A1)-(\dx,0)$);

\filldraw 
   (A1)
   circle  (\r pt)
   node[below] {\small{$A_1$}};

\filldraw
   (A2)
   circle  (\r pt)
   node[below] {\small{$A_2$}};

   
\filldraw 
   (Ak)
   circle  (\r pt)
   node[below] {\small{$A_k$}};

\coordinate (S12) at ($(A1)+    (V1)$);
\filldraw  (S12) circle  (\r pt);
\coordinate (S22) at ($(A1)+    (V2)$);
\filldraw  (S22) circle  (\r pt);

\coordinate (S13) at ($(A1)+    2*(V1)$);
\coordinate (S23) at ($(A1)+    2*(V2)$);

\coordinate (S1k) at ($(A1)+  3.0*(V1)$);
\coordinate (S2k) at ($(A1)+  3.0*(V2)$);
\coordinate (S1kk) at ($(A1)+  4.0*(V1)$);
\coordinate (S2kk) at ($(A1)+  4.0*(V2)$);
\filldraw  (S2k) circle  (\r pt);
\filldraw  (S1k) circle  (\r pt);

\coordinate (S14) at ($(A1)-  1.0*(V1)$);
\coordinate (S24) at ($(A1)-  1.0*(V2)$);

\draw []
   (S1kk)
   node[anchor=south] {$r_2$}
   --
   (S14);
\draw []
   (S2kk)
   node[anchor=south] {$r_m$}
   --
   (S24);