document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=757173>Question 757173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in g p if sum of first two digits is 7 and sum of first 6 digits is 91 then what is the sum of first 4 digits<BR>\n" );
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 #460697 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=460697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You must mean \"numbers\" and not \"digits\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Geometric Progression: a, ar, ar^2, ar^3,...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar=7 ALIGN=MIDDLE  ALT=\"a%2Bar=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar%2Bar%5E2%2Bar%5E3%2Bar%5E4%2Bar%5E5=91 ALIGN=MIDDLE  ALT=\"a%2Bar%2Bar%5E2%2Bar%5E3%2Bar%5E4%2Bar%5E5=91\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar%2Bar%5E2%2Bar%5E3 ALIGN=MIDDLE  ALT=\"a%2Bar%2Bar%5E2%2Bar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "91 is perfectly divisible by 7, and their corresponding polynomial expressions are also well-dividible.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What happens?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bar%2Bar%5E2%2Bar%5E3%2Bar%5E4%2Bar%5E5%29%2F%28a%2Bar%29=91%2F7 ALIGN=MIDDLE  ALT=\"%28a%2Bar%2Bar%5E2%2Bar%5E3%2Bar%5E4%2Bar%5E5%29%2F%28a%2Bar%29=91%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%5E5%2Br%5E4%2Br%5E3%2Br%5E2%2Br%2B1%29%2F%28r%2B1%29=13 ALIGN=MIDDLE  ALT=\"%28r%5E5%2Br%5E4%2Br%5E3%2Br%5E2%2Br%2B1%29%2F%28r%2B1%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Perform your division and find:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E4%2Br%5E2%2B1=13 ALIGN=MIDDLE  ALT=\"r%5E4%2Br%5E2%2B1=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "from which <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E4%2Br%5E2-12=0 ALIGN=MIDDLE  ALT=\"r%5E4%2Br%5E2-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which IS factorable.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28r%5E2-3%29%28r%5E2%2B4%29=0%29 ALIGN=MIDDLE  ALT=\"highlight%28%28r%5E2-3%29%28r%5E2%2B4%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We want REAL solutions for r, not complex with imaginaries.  Focus on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-3 ALIGN=MIDDLE  ALT=\"r%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=3 ALIGN=MIDDLE  ALT=\"r%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2B-+sqrt%283%29 ALIGN=MIDDLE  ALT=\"r=%2B-+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Further steps from this and using the given a+ar=7 give that:<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%283%29 ALIGN=MIDDLE  ALT=\"r=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%287%2Asqrt%283%29-7%29%2F2 ALIGN=MIDDLE  ALT=\"a=%287%2Asqrt%283%29-7%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"r=-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-%287%2B7%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"a=-%287%2B7%2Asqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take your pick and form your sum to four terms and find what that sum is.  Just some messy steps to keep track.<BR>\n" );
document.write( "(do not be mislead from the abbreviated work shown here.  More details went onto paper and I spent about 35 minutes  to 45 minutes doing the steps and also typing this text-based posted solution.  ) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );