document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083503>Question 1083503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the arithmetic series : 12+18+24+....+2880<BR>\n" );
document.write( "Calculate the sum of all the terms of the series tht are not visible by 4 \r<BR>\n" );
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document.write( "6x+12;2x+4;andx-7 are the first three terms of a geometric sequence<BR>\n" );
document.write( "Solve for x\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697516 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The common difference is 6, and A\all terms are divisible by 6,<BR>\n" );
document.write( "from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A2=12=4%2A3 ALIGN=MIDDLE  ALT=\"6%2A2=12=4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A480=2880=4%2A180%2A6 ALIGN=MIDDLE  ALT=\"6%2A480=2880=4%2A180%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "First and last terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2880 ALIGN=MIDDLE  ALT=\"2880\"   DISABLED_style= \"max-width:90%; height:auto;\" > are divisible by 4.<BR>\n" );
document.write( "However, with a common difference of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=3%2A2 ALIGN=MIDDLE  ALT=\"6=3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "every other term will be not divisible by 4.<BR>\n" );
document.write( "Those terms from an arithmetic series with common difference <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A2=12 ALIGN=MIDDLE  ALT=\"6%2A2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=6%2A3=18 ALIGN=MIDDLE  ALT=\"a%5B1%5D=6%2A3=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=6%2A479=2874 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=6%2A479=2874\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The difference between first and last term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D-a%5B1%5D=12%28n-1%29=6%2A479-6%2A3=6%28479-3%29=6%2A476=6%2A2%2A238=12%2A238 ALIGN=MIDDLE  ALT=\"a%5Bn%5D-a%5B1%5D=12%28n-1%29=6%2A479-6%2A3=6%28479-3%29=6%2A476=6%2A2%2A238=12%2A238\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1=238 ALIGN=MIDDLE  ALT=\"n-1=238\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=239 ALIGN=MIDDLE  ALT=\"n=239\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2=239%2818%2B2874%29%2F2=239%2A2892%2F2=highlight%28345594%29 ALIGN=MIDDLE  ALT=\"n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2=239%2818%2B2874%29%2F2=239%2A2892%2F2=highlight%28345594%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The common ratio of that geometric sequence is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%2F%282x%2B4%29=%282x%2B4%29%2F%286x%2B12%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%2F%282x%2B4%29=%282x%2B4%29%2F%286x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%2F%282x%2B4%29=%282x%2B4%29%2F%286x%2B12%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%2F%282x%2B4%29=%282x%2B4%29%2F%286x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%2F%282%28x%2B2%29%29=%282x%2B4%29%2F%286%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%2F%282%28x%2B2%29%29=%282x%2B4%29%2F%286%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Denominators require <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%3C%3E0%29 ALIGN=MIDDLE  ALT=\"x%2B2%3C%3E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-2 ALIGN=MIDDLE  ALT=\"x%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x%2B2%29 ALIGN=MIDDLE  ALT=\"12%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we gw=et<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28x-7%29=2%282x%2B4%29 ALIGN=MIDDLE  ALT=\"6%28x-7%29=2%282x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-42%29=4x%2B8 ALIGN=MIDDLE  ALT=\"6x-42%29=4x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-4x=42%2B8 ALIGN=MIDDLE  ALT=\"6x-4x=42%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=50 ALIGN=MIDDLE  ALT=\"2x=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=25%29 ALIGN=MIDDLE  ALT=\"highlight%28x=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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