document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773910>Question 773910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of first 4 terms of Geometric progression is 7.5 if the sum of middle two terms is 3 find the terms of gp </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471934 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "the sum of first 4 terms of Geometric progression is 7.5 if the sum of middle two terms is 3 find the terms of gp<BR>\n" );
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document.write( "A:<BR>\n" );
document.write( "Let x = first term<BR>\n" );
document.write( "and r = common ratio<BR>\n" );
document.write( "Therefore, rx = second term<BR>\n" );
document.write( "           <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2x ALIGN=MIDDLE  ALT=\"r%5E2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = third term<BR>\n" );
document.write( "           <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3x ALIGN=MIDDLE  ALT=\"r%5E3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = fourth term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+rx+%2B+r%5E2x+%2B+r%5E3x ALIGN=MIDDLE  ALT=\"x+%2B+rx+%2B+r%5E2x+%2B+r%5E3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281+%2B+r%29+%2B+r%5E2x%281+%2B+r%29 ALIGN=MIDDLE  ALT=\"x%281+%2B+r%29+%2B+r%5E2x%281+%2B+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+%2B+r%29%28x+%2B+r%5E2x%29 ALIGN=MIDDLE  ALT=\"%281+%2B+r%29%28x+%2B+r%5E2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281+%2B+r%29%281+%2B+r%5E2%29 ALIGN=MIDDLE  ALT=\"x%281+%2B+r%29%281+%2B+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.5<BR>\n" );
document.write( "The sum of the middle two terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rx+%2B+r%5E2x ALIGN=MIDDLE  ALT=\"rx+%2B+r%5E2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3  ---> rx(1 + r) = 3   ---> x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fr%281%2Br%29 ALIGN=MIDDLE  ALT=\"3%2Fr%281%2Br%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Fr%281%2Br%29%29%281+%2B+r%29%281+%2B+r%5E2%29 ALIGN=MIDDLE  ALT=\"%283%2Fr%281%2Br%29%29%281+%2B+r%29%281+%2B+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Fr%28cross%281%2Br%29%29%29%28cross%281+%2B+r%29%29%281+%2B+r%5E2%29 ALIGN=MIDDLE  ALT=\"%283%2Fr%28cross%281%2Br%29%29%29%28cross%281+%2B+r%29%29%281+%2B+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+r%5E2 ALIGN=MIDDLE  ALT=\"1+%2B+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5%28r%2F3%29 ALIGN=MIDDLE  ALT=\"7.5%28r%2F3%29\"   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+-+2.5r+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"r%5E2+-+2.5r+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%5E2+-+5r+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"2r%5E2+-+5r+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2r - 1)(r - 1) = 0<BR>\n" );
document.write( "r = <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;\" > or r = 1, disregard r = 1<BR>\n" );
document.write( "If r = 1/2, then x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%281%2F2%29%281%2B%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"3%2F%281%2F2%29%281%2B%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4<BR>\n" );
document.write( "The first term is 4, to get the next term, multiply by the common ratio 1/2.<BR>\n" );
document.write( "The first 4 terms are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284%29 ALIGN=MIDDLE  ALT=\"highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "       </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );