document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878901>Question 878901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 5, x, y, z, 405 are the first term of a GP , find the value of x, y, z. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530371 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=530371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a GP (a geometric progression or geometric sequence) each term is equal to the previous multiplied times a constant often called the common factor and represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "MENTAL MATH (not showing the works of your quick mind):<BR>\n" );
document.write( "The GP started with 5, and after multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > four times we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%5E4=405=810%2F2=10%2A81%2F2%2A5=5%2A81=5%2A3%5E4 ALIGN=MIDDLE  ALT=\"5r%5E4=405=810%2F2=10%2A81%2F2%2A5=5%2A81=5%2A3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which makes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2A3=highlight%2815%29 ALIGN=MIDDLE  ALT=\"x=5%2A3=highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%2A3=highlight%2845%29 ALIGN=MIDDLE  ALT=\"x=15%2A3=highlight%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=45%2A3=highlight%28135%29 ALIGN=MIDDLE  ALT=\"y=45%2A3=highlight%28135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=135%2A3=highlight%28405%29 ALIGN=MIDDLE  ALT=\"z=135%2A3=highlight%28405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "SHOW YOUR WORK:<BR>\n" );
document.write( "Teachers like to see formulas, and formulas are an efficient way to describe ideas and concepts. What you can think through in 5 seconds can be written in formulas in 5 minutes, while it would take much longer to write an explanation of the calculations in paragraph form. However, using formulas to communicate requires sharing a common symbolic language, and we may be used to different languages.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= first term of the GP.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common ratio of the GP.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D=b%5B1%5Dr%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"b%5Bn%5D=b%5B1%5Dr%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5Eth ALIGN=MIDDLE  ALT=\"n%5Eth\"   DISABLED_style= \"max-width:90%; height:auto;\" >  term of the GP.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=5 ALIGN=MIDDLE  ALT=\"b%5B1%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B5%5D=405 ALIGN=MIDDLE  ALT=\"b%5B5%5D=405\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%5E%285-1%29=405 ALIGN=MIDDLE  ALT=\"5r%5E%285-1%29=405\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%5E4=405 ALIGN=MIDDLE  ALT=\"5r%5E4=405\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E4=405%2F5 ALIGN=MIDDLE  ALT=\"r%5E4=405%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E4=81 ALIGN=MIDDLE  ALT=\"r%5E4=81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=root%284%2C81%29 ALIGN=MIDDLE  ALT=\"r=root%284%2C81%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=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=b%5B2%5D=5%2A3%5E%282-1%29=5%2A3%5E1=5%2A3=highlight%2815%29 ALIGN=MIDDLE  ALT=\"x=b%5B2%5D=5%2A3%5E%282-1%29=5%2A3%5E1=5%2A3=highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=b%5B3%5D=5%2A3%5E%283-1%29=5%2A3%5E2=5%2A9=highlight%2845%29 ALIGN=MIDDLE  ALT=\"y=b%5B3%5D=5%2A3%5E%283-1%29=5%2A3%5E2=5%2A9=highlight%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=b%5B4%5D=5%2A3%5E%284-1%29=5%2A3%5E3=5%2A27=highlight%28135%29 ALIGN=MIDDLE  ALT=\"z=b%5B4%5D=5%2A3%5E%284-1%29=5%2A3%5E3=5%2A27=highlight%28135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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