A slight generalization of Raaja's and TeXncian's answers in that I allow arbitrary color cycle lists, which is illustrated by an additional list of length 3.

documentclass[tikz,border=3.14mm]standalone
begindocument
begintikzpicture
deflstColors"red!70","yellow!50"
foreach X [evaluate=X as Col using lstColors[int(mod(X,2))]] in 1,...,20
draw[line width = 8pt,Col] (0,0) circle (X);
endtikzpicture
begintikzpicture
deflstColors"red!70","yellow!50","blue!70"
foreach X [evaluate=X as Col using lstColors[int(mod(X,3))]] in 1,...,20
draw[line width = 8pt,Col] (0,0) circle (X);
endtikzpicture
enddocument

A PSTricks solution.

documentclass[pstricks]standalone
pssetrunit=4pt,unit=psrunit
begindocument
pspicture[linewidth=.5](-11,-11)(11,11)
 foreach i in 1,2,...,10%
 ifoddidefcyellowelsedefcredfi
 pscircle[linecolor=c]i
endpspicture
enddocument

Note: There is an unnecessary white spot after converting to PNG.

Animated version

documentclass[pstricks]standalone
pssetrunit=4pt,unit=psrunit
begindocument 
foreach j in 1,...,10%
pspicture[linewidth=.5](-11,-11)(11,11)
 foreach i in 1,...,j%
 ifoddidefcyellowelsedefcredfi
 pscircle[linecolor=c]i%
endpspicture
enddocument

This is Raaja's solution but without the second loop (test if the count variable is odd) and with a simple draw instead of nodes (change line width to make it thicker).

documentclassstandalone
usepackagetikz

begindocument
begintikzpicture[mystyle/.style=circle,draw,fill=none,minimum size=20, line width = 8pt]
 foreach x in 1,...,20
 pgfmathparseisodd(x)ifnumpgfmathresult=1defcurrcolred!70elsedefcurrcolyellow!50fi
 draw[line width=8pt,currcol] (0,0) circle (x cm);
endtikzpicture
enddocument 

A SkiaSharp solution only for comparison purposes.

using SkiaSharp; // needs skiasharp nuget
using System.Diagnostics;


class ConcentricCircle

 static readonly SKPaint yellowStroke = new SKPaint
 
 Style = SKPaintStyle.Stroke,
 Color = SKColors.Yellow,
 IsAntialias = true
 ;


 static readonly SKPaint redStroke = new SKPaint
 
 Style = SKPaintStyle.Stroke,
 Color = SKColors.Red,
 IsAntialias = true
 ;

 static readonly float scale = SKDocument.DefaultRasterDpi / 2.54f; // dots per cm
 static readonly float width = 6 * scale; // 6 cm
 static readonly float height = 6 * scale; // 6 cm

 static float PtToCm(float pt) => pt / scale;



 public static void Generate(string filename)
 
 yellowStroke.StrokeWidth = PtToCm(4); // 4pt
 redStroke.StrokeWidth = PtToCm(4); // 4pt

 using (var stream = new SKFileWStream($"filename.pdf"))
 using (var document = SKDocument.CreatePdf(stream))
 using (var canvas = document.BeginPage(width, height))
 

 // translate first and then scale, don't reverse!
 canvas.Translate(width / 2, height / 2);
 canvas.Scale(scale);

 // draw a red circle
 for (int i = 0; i < 5; i++)
 
 canvas.DrawCircle(0, 0, PtToCm(8) * (2 * i + 1), yellowStroke);
 canvas.DrawCircle(0, 0, PtToCm(8) * (2 * i + 2), redStroke);
 

 document.EndPage();
 
 

 private static void Main()
 
 string filename = nameof(ConcentricCircle);
 Generate(filename);

 // convert to PNG with ImageMagick
 using (Process p = new Process())
 
 p.StartInfo.FileName = "magick";
 p.StartInfo.Arguments = $"convert -compose copy -bordercolor red -border 2x2 -density 200 -alpha remove filename.pdf filename.png";
 p.Start();
 
 

Just for fun. Another solution which draws a couple of red and yellow circles in each iteration:

documentclass[tikz,border=3mm]standalone

usetikzlibrarypositioning

begindocument
begintikzpicture[
 mycircle/.style=circle, draw, fill=none, line width=8pt,
 twocircle/.style=
 mycircle,
 minimum size=#1cm,
 color=yellow!70,
 append after command=%
 pgfextra
 node[mycircle, minimum size=thenumexpr#1-1relax cm, color=red!70] at (tikzlastnode.center) ;
 endpgfextra,
]

foreach i in 2,4,...,12
 node[twocircle=i] ;
endtikzpicture
enddocument

A slightly different approach to the solution proposed @TeXnician (suggested by this: What is wrong with the use of `isodd` of `xifthen`?):

documentclassstandalone
usepackagetikz

begindocument
begintikzpicture[mystyle/.style=circle,draw,fill=none,minimum size=20, line width = 8pt]
 foreach x in 1,2,...,19
 pgfmathsetmacromycolorisodd x?"red!70":"yellow!50"%
 node [mystyle, minimum size = x cm, mycolor] (2) at (0, 0) ;
 %
endtikzpicture
enddocument