document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138563>Question 1138563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/2,2/5,1,   <BR>\n" );
document.write( "What's the sixth term of sequence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756385 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "first find differences to see what formula we need\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....\r<BR>\n" );
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document.write( "...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F10 ALIGN=MIDDLE  ALT=\"-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ....\r<BR>\n" );
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document.write( "............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........2nd difference tells us we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=quadratic ALIGN=MIDDLE  ALT=\"quadratic\"   DISABLED_style= \"max-width:90%; height:auto;\" > sequence, so we need\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=an%5E2%2Bbn%2Bc ALIGN=MIDDLE  ALT=\"a%5Bn%5D=an%5E2%2Bbn%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use given terms to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=1%2F2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=a%2A1%5E2%2Bb%2A1%2Bc ALIGN=MIDDLE  ALT=\"1%2F2=a%2A1%5E2%2Bb%2A1%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=a%2Bb%2Bc ALIGN=MIDDLE  ALT=\"1%2F2=a%2Bb%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=2%2F5 ALIGN=MIDDLE  ALT=\"a%5B2%5D=2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2 ALIGN=MIDDLE  ALT=\"n=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5=a%2A2%5E2%2Bb%2A2%2Bc ALIGN=MIDDLE  ALT=\"2%2F5=a%2A2%5E2%2Bb%2A2%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5=4a%2B2b%2Bc ALIGN=MIDDLE  ALT=\"2%2F5=4a%2B2b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=20a%2B10b%2B5c ALIGN=MIDDLE  ALT=\"2=20a%2B10b%2B5c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=1 ALIGN=MIDDLE  ALT=\"a%5B3%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=3 ALIGN=MIDDLE  ALT=\"n=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=a%2A3%5E2%2Bb%2A3%2Bc ALIGN=MIDDLE  ALT=\"1=a%2A3%5E2%2Bb%2A3%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=9a%2B3b%2Bc ALIGN=MIDDLE  ALT=\"1=9a%2B3b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.3\r<BR>\n" );
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document.write( "subtract eq.1 from eq.3 :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2F2=9a-a%2B3b-b%2Bc-c ALIGN=MIDDLE  ALT=\"1-1%2F2=9a-a%2B3b-b%2Bc-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=8a%2B2b ALIGN=MIDDLE  ALT=\"1%2F2=8a%2B2b\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2-8a=2b ALIGN=MIDDLE  ALT=\"1%2F2-8a=2b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%281%2F2-8a%29%2F2 ALIGN=MIDDLE  ALT=\"b=%281%2F2-8a%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F4-4a ALIGN=MIDDLE  ALT=\"b=1%2F4-4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.1a\r<BR>\n" );
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document.write( "plug in eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=20a%2B10%281%2F4-4a%29%2B5c ALIGN=MIDDLE  ALT=\"2=20a%2B10%281%2F4-4a%29%2B5c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=20a%2B5%2F2-40a%2B5c ALIGN=MIDDLE  ALT=\"2=20a%2B5%2F2-40a%2B5c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=5%2F2-20a%2B5c ALIGN=MIDDLE  ALT=\"2=5%2F2-20a%2B5c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-5%2F2%2B20a=5c ALIGN=MIDDLE  ALT=\"2-5%2F2%2B20a=5c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=20a%2F5%2B2%2F5-%285%2F2%29%2F5 ALIGN=MIDDLE  ALT=\"c=20a%2F5%2B2%2F5-%285%2F2%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4a%2B2%2F5-5%2F10 ALIGN=MIDDLE  ALT=\"c=4a%2B2%2F5-5%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4a-1%2F10 ALIGN=MIDDLE  ALT=\"c=4a-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >............eq.2a\r<BR>\n" );
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document.write( "go to eq.1, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > from eq.1a and eq.2a\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=a%2B%281%2F4-4a%29%2B%284a-1%2F10%29 ALIGN=MIDDLE  ALT=\"1%2F2=a%2B%281%2F4-4a%29%2B%284a-1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=a%2B1%2F4-cross%284a%29%2Bcross%284a%29-1%2F10 ALIGN=MIDDLE  ALT=\"1%2F2=a%2B1%2F4-cross%284a%29%2Bcross%284a%29-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=a%2B1%2F4-1%2F10 ALIGN=MIDDLE  ALT=\"1%2F2=a%2B1%2F4-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=a%2B3%2F20 ALIGN=MIDDLE  ALT=\"1%2F2=a%2B3%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2-3%2F20=a ALIGN=MIDDLE  ALT=\"1%2F2-3%2F20=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10%2F20-3%2F20 ALIGN=MIDDLE  ALT=\"a=10%2F20-3%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=7%2F20 ALIGN=MIDDLE  ALT=\"a=7%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F4-4a ALIGN=MIDDLE  ALT=\"b=1%2F4-4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.1a, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F4-4%287%2F20%29 ALIGN=MIDDLE  ALT=\"b=1%2F4-4%287%2F20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F4-7%2F5 ALIGN=MIDDLE  ALT=\"b=1%2F4-7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-23%2F20 ALIGN=MIDDLE  ALT=\"b=-23%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4a-1%2F10 ALIGN=MIDDLE  ALT=\"c=4a-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >............eq.2a, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4%287%2F20%29-1%2F10 ALIGN=MIDDLE  ALT=\"c=4%287%2F20%29-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7%2F5-1%2F10 ALIGN=MIDDLE  ALT=\"c=7%2F5-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=13%2F10 ALIGN=MIDDLE  ALT=\"c=13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+7%2F20 ALIGN=MIDDLE  ALT=\"a+=+7%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-23%2F20 ALIGN=MIDDLE  ALT=\"+b+=+-23%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+13%2F10 ALIGN=MIDDLE  ALT=\"c+=+13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> nth term formula is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=%287%2F20%29n%5E2-%2823%2F20%29n%2B13%2F10 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=%287%2F20%29n%5E2-%2823%2F20%29n%2B13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now, you need to find the sixth term of sequence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D ALIGN=MIDDLE  ALT=\"a%5B6%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=%287%2F20%296%5E2-%2823%2F20%296%2B13%2F10 ALIGN=MIDDLE  ALT=\"a%5B6%5D=%287%2F20%296%5E2-%2823%2F20%296%2B13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=%287%2F20%2936-%2823%2F20%296%2B13%2F10 ALIGN=MIDDLE  ALT=\"a%5B6%5D=%287%2F20%2936-%2823%2F20%296%2B13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=%287%2F5%299-%2823%2F10%293%2B13%2F10 ALIGN=MIDDLE  ALT=\"a%5B6%5D=%287%2F5%299-%2823%2F10%293%2B13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=63%2F5-69%2F10%2B13%2F10 ALIGN=MIDDLE  ALT=\"a%5B6%5D=63%2F5-69%2F10%2B13%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=139%2F10-69%2F10 ALIGN=MIDDLE  ALT=\"a%5B6%5D=139%2F10-69%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=70%2F10 ALIGN=MIDDLE  ALT=\"a%5B6%5D=70%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=7 ALIGN=MIDDLE  ALT=\"a%5B6%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );