document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118821>Question 118821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the geometric sequence the first three terms are ( 5x-8,3x,2x+2,...).What is the value of x ? Please help me :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86942 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=86942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the value of x if the first three terms of a geometric sequence are given as:<BR>\n" );
document.write( "{5x-8, 3x, 2x+2,...}<BR>\n" );
document.write( "You know that in a geometric sequence, consecutive terms have a common ratio.<BR>\n" );
document.write( "This can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D%2Fa%5Bn-1%5D++=+k ALIGN=MIDDLE  ALT=\"a%5Bn%5D%2Fa%5Bn-1%5D++=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > or, in words...Any term divided by the previous term is a constant called the common ratio, r.<BR>\n" );
document.write( "So, let's use this useful fact to find x in your problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F%285x-8%29+=+k ALIGN=MIDDLE  ALT=\"3x%2F%285x-8%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B2%29%2F3x+=+k ALIGN=MIDDLE  ALT=\"%282x%2B2%29%2F3x+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, since k = k, we can set these two equal to each other:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F%285x-8%29+=+%282x%2B2%29%2F3x ALIGN=MIDDLE  ALT=\"3x%2F%285x-8%29+=+%282x%2B2%29%2F3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%283x%29+=+%285x-8%29%282x%2B2%29 ALIGN=MIDDLE  ALT=\"3x%283x%29+=+%285x-8%29%282x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+=+10x%5E2-6x-16 ALIGN=MIDDLE  ALT=\"9x%5E2+=+10x%5E2-6x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2 ALIGN=MIDDLE  ALT=\"9x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2-6x-16 ALIGN=MIDDLE  ALT=\"0+=+x%5E2-6x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >Solve this quadratic equation by factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-8%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product principle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+=+0 ALIGN=MIDDLE  ALT=\"x%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8+=+0 ALIGN=MIDDLE  ALT=\"x-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+=+0 ALIGN=MIDDLE  ALT=\"x%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8+=+0 ALIGN=MIDDLE  ALT=\"x-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So there are two possible solutions for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since the problem does not give us the common ratio, both values of x are valid solutions.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "{5x-8, 3x, 2x+2,...} Let's try x = -2<BR>\n" );
document.write( "{5(-2)-8, 3(-2), 2(-2)+2,...}<BR>\n" );
document.write( "{-18, -6, -2,...} The common ratio, r, is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2F-18+=+1%2F3 ALIGN=MIDDLE  ALT=\"-6%2F-18+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F-6+=+1%2F3 ALIGN=MIDDLE  ALT=\"-2%2F-6+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK<BR>\n" );
document.write( "Now try x = 8:<BR>\n" );
document.write( "{5x-8, 3x, 2x+2,...}<BR>\n" );
document.write( "{5(8)-8, 3(8), 2(8)+2,...}<BR>\n" );
document.write( "{32, 24, 18,...} The common ratio here is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F32+=+3%2F4 ALIGN=MIDDLE  ALT=\"24%2F32+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F24+=+3%2F4 ALIGN=MIDDLE  ALT=\"18%2F24+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK </SPAN>\n" );
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