document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662303>Question 662303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first three terms of a geometric series are p-1, 2p, and 4p +6 respectively where p is a constant<BR>\n" );
document.write( "(a) find the value of the constant p<BR>\n" );
document.write( "(b) calculate the corresponding value of the common ratio<BR>\n" );
document.write( "(c) Find the sum to ten terms of the series </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412190 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=412190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The common ratio, is the ratio between consecutive terms in a geometric sequence, and it is constant, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2p%2F%28p-1%29=%284p%2B6%29%2F2p ALIGN=MIDDLE  ALT=\"2p%2F%28p-1%29=%284p%2B6%29%2F2p\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2=%28p-1%29%284p%2B6%29 ALIGN=MIDDLE  ALT=\"4p%5E2=%28p-1%29%284p%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equating the cross-products<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2=%28p-1%29%284p%2B6%29 ALIGN=MIDDLE  ALT=\"4p%5E2=%28p-1%29%284p%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2=4p%5E2%2B2p-6 ALIGN=MIDDLE  ALT=\"4p%5E2=4p%5E2%2B2p-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2p-6 ALIGN=MIDDLE  ALT=\"0=2p-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2p=6 ALIGN=MIDDLE  ALT=\"2p=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=3%29 ALIGN=MIDDLE  ALT=\"highlight%28p=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The first three terms are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-1=3-1=2 ALIGN=MIDDLE  ALT=\"p-1=3-1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2p=2%2A3=6 ALIGN=MIDDLE  ALT=\"2p=2%2A3=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%2B6=4%2A3%2B6=12%2B6=18 ALIGN=MIDDLE  ALT=\"4p%2B6=4%2A3%2B6=12%2B6=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The common ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2=highlight%283%29 ALIGN=MIDDLE  ALT=\"6%2F2=highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The sum of the first <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 of a geometric sequence with first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A%28%28r%5En-1%29%2F%28r-1%29%29 ALIGN=MIDDLE  ALT=\"a%2A%28%28r%5En-1%29%2F%28r-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28%283%5E10-1%29%2F%283-1%29%29=2%2A%2859049-1%29%2F2=highlight%2859048%29 ALIGN=MIDDLE  ALT=\"2%2A%28%283%5E10-1%29%2F%283-1%29%29=2%2A%2859049-1%29%2F2=highlight%2859048%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );