document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010896>Question 1010896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sum of the first 6 terms of a geometric progression equals to 63. <BR>\n" );
document.write( "Sum of the even terms equals to 42.<BR>\n" );
document.write( "What's the common ratio and the initial value?\r<BR>\n" );
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document.write( "Simply wrote, it's<BR>\n" );
document.write( "s6=63<BR>\n" );
document.write( "a2+a4+a6=42<BR>\n" );
document.write( "a1=?<BR>\n" );
document.write( "r=?\r<BR>\n" );
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document.write( "Sum of the odd numbers therefore is A1+A3+A5=21.<BR>\n" );
document.write( "I expand a2+a4+a6=42 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a1%2Ar%2Ba1%2Ar%5E3%2Ba1%2Ar%5E5=42 ALIGN=MIDDLE  ALT=\"a1%2Ar%2Ba1%2Ar%5E3%2Ba1%2Ar%5E5=42\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a1+a3+a5=21 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a1%2Ba1%2Ar%5E2%2Ba1%2Ar%5E4=21 ALIGN=MIDDLE  ALT=\"a1%2Ba1%2Ar%5E2%2Ba1%2Ar%5E4=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I can further simplify it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a1%2A%28r%2Br%5E3%2Br%5E5%29=42 ALIGN=MIDDLE  ALT=\"a1%2A%28r%2Br%5E3%2Br%5E5%29=42\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a1%2A%281%2Br%5E2%2Br%5E4%29=21 ALIGN=MIDDLE  ALT=\"a1%2A%281%2Br%5E2%2Br%5E4%29=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I have no idea how to progress further. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626410 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=626410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An=A1 r^(n-1)<BR>\n" );
document.write( "A6=A1*r^(n-1);63=A1*r^(5)<BR>\n" );
document.write( "A1(r+r^3+r^5)=2A1(1+r^2+r^4)<BR>\n" );
document.write( "r^5-2r^4+r^3-2r^2+r-2=0<BR>\n" );
document.write( "By synthetic division or graphing, r=2.<BR>\n" );
document.write( "Sn=A1(1-r^6)/1-2<BR>\n" );
document.write( "63=A1(1-64)/-1<BR>\n" );
document.write( "63=63A1<BR>\n" );
document.write( "A1=1<BR>\n" );
document.write( "A2=2<BR>\n" );
document.write( "A3=4<BR>\n" );
document.write( "A4=8<BR>\n" );
document.write( "A5=16<BR>\n" );
document.write( "A6=32<BR>\n" );
document.write( "initial value is 1<BR>\n" );
document.write( "common ratio is 2\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );