document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=648175>Question 648175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you explain the solution to this problem please?\r<BR>\n" );
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document.write( "In a G.P. the sum of the 2nd and 3rd terms is 6, the sum of the 3rd and 4th terms is -12. Find the 1st term and the common ratio.\r<BR>\n" );
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document.write( "Thanks very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406754 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Can you explain the solution to this problem please?\r<BR>\n" );
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document.write( "In a G.P. the sum of the 2nd and 3rd terms is 6, the sum of the 3rd and 4th terms is -12. Find the 1st term and the common ratio.\r<BR>\n" );
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document.write( "Thanks very much\r<BR>\n" );
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document.write( "GP formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%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=a%5B2%5D+=+a%5B1%5Dr%5E%282+-+1%29 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%5B1%5Dr%5E%282+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%5B1%5Dr ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%5B1%5Dr\"   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%5B3%5D+=+a%5B1%5Dr%5E%283+-+1%29 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+a%5B1%5Dr%5E%283+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+a%5B1%5Dr%5E2 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+a%5B1%5Dr%5E2\"   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%5B4%5D+=+a%5B1%5Dr%5E%284+-+1%29 ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+a%5B1%5Dr%5E%284+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D+=+a%5B1%5Dr%5E3+ ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+a%5B1%5Dr%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since terms 2 and 3 sum to 6, then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5Dr+%2B+a%5B1%5Dr%5E2+=+6 ALIGN=MIDDLE  ALT=\"a%5B1%5Dr+%2B+a%5B1%5Dr%5E2+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%28r+%2B+r%5E2%29+=+6 ALIGN=MIDDLE  ALT=\"a%5B1%5D%28r+%2B+r%5E2%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+6%2F%28r%5E2+%2B+r%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+6%2F%28r%5E2+%2B+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- eq (i)\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+6+-+a%5B1%5Dr ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+6+-+a%5B1%5Dr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D+=+a%5B1%5Dr%5E3 ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+a%5B1%5Dr%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+%2B+a%5B4%5D+=+-+12 ALIGN=MIDDLE  ALT=\"a%5B3%5D+%2B+a%5B4%5D+=+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+-+a%5B1%5Dr+%2B+a%5B1%5Dr%5E3+=+-+12 ALIGN=MIDDLE  ALT=\"6+-+a%5B1%5Dr+%2B+a%5B1%5Dr%5E3+=+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ eq (ii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5Dr%5E3+-+a%5B1%5Dr+=+-+18 ALIGN=MIDDLE  ALT=\"a%5B1%5Dr%5E3+-+a%5B1%5Dr+=+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ eq (ii)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F%28r%5E2+%2B+r%29%29+%2A+r%5E3+-+%286%2F%28r%5E2+%2B+r%29%29+%2A+r+=+-+18 ALIGN=MIDDLE  ALT=\"%286%2F%28r%5E2+%2B+r%29%29+%2A+r%5E3+-+%286%2F%28r%5E2+%2B+r%29%29+%2A+r+=+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28r%5E2+%2B+r%29 ALIGN=MIDDLE  ALT=\"6%2F%28r%5E2+%2B+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > in eq (ii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F%28r%28r+%2B+1%29%29%29+%2A+r%5E3+-+%286%2F%28r%28r+%2B+1%29%29%29+%2A+r+=+-+18 ALIGN=MIDDLE  ALT=\"%286%2F%28r%28r+%2B+1%29%29%29+%2A+r%5E3+-+%286%2F%28r%28r+%2B+1%29%29%29+%2A+r+=+-+18\"   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=%286%2F%28cross%28r%29%28r+%2B+1%29%29%29+%2A+r%5E2%28cross%28r%5E3%29%29+-+%286%2F%28cross%28r%29%28r+%2B+1%29%29%29+%2A+cross%28r%29+=+-+18 ALIGN=MIDDLE   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=%286r%5E2%29%2F%28r+%2B+1%29+-+6%2F%28r+%2B+1%29+=+-+18 ALIGN=MIDDLE  ALT=\"%286r%5E2%29%2F%28r+%2B+1%29+-+6%2F%28r+%2B+1%29+=+-+18\"   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=6r%5E2+-+6+=+-+18%28r+%2B+1%29 ALIGN=MIDDLE  ALT=\"6r%5E2+-+6+=+-+18%28r+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Multiplying by LCD, r + 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6r%5E2+%2B+18r+%2B+12+=+0 ALIGN=MIDDLE  ALT=\"6r%5E2+%2B+18r+%2B+12+=+0\"   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=6%28r%5E2+%2B+3r+%2B+2%29+=+2%280%29 ALIGN=MIDDLE  ALT=\"6%28r%5E2+%2B+3r+%2B+2%29+=+2%280%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=r%5E2+%2B+3r+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"r%5E2+%2B+3r+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(r + 2)(r + 1) = 0\r<BR>\n" );
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document.write( "r = - 2 or – 1\r<BR>\n" );
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document.write( "======<BR>\n" );
document.write( "Check<BR>\n" );
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document.write( "r = - 2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%28-+2%29%5E2+%2B+a%5B1%5D%28-+2%29+=+6 ALIGN=MIDDLE  ALT=\"a%5B1%5D%28-+2%29%5E2+%2B+a%5B1%5D%28-+2%29+=+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=4a%5B1%5D+-+2a%5B1%5D+=+6 ALIGN=MIDDLE  ALT=\"4a%5B1%5D+-+2a%5B1%5D+=+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=2a%5B1%5D+=+6 ALIGN=MIDDLE  ALT=\"2a%5B1%5D+=+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%5B1%5D+=+3 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+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=highlight_green%28r+=+-+2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r+=+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; First term, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283%29 ALIGN=MIDDLE  ALT=\"highlight_green%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "r = - 1<BR>\n" );
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