document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114522>Question 1114522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man gets a rise of 10% in salary at the end of his first year of service, and further rises of 20% and 25% at the end of the second and third years respectively,the rise in each case being calculated on his salary at the beginning of the year. Find geometric mean. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729526 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it's been a while, so i forgot what a geometric mean is.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "fortunately there are references on the web that can help.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.mathsisfun.com/numbers/geometric-mean.html\" target = \"_blank\">http://www.mathsisfun.com/numbers/geometric-mean.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on your description of the problem, you have a series of numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the first number is x, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the second number is 1.1 * x.<BR>\n" );
document.write( "the third number is 1.2 * 1.1 * x.<BR>\n" );
document.write( "the fourth number is 1.25 * 1.2 * 1.1 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is based on my understanding that each year's increase is based on the salary at the beginning of that year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the geometric means would therefore be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the fourth root of (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes the fourth foot of (1.1^3 * 1.2^2 * 1.25 * x^4).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes equal to the fourth root of (1.1^3 * 1.2^2 * 1.25) * x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes equal to the fourth root of (2.3958) * x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes equal to 1.244121056 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if this is true, then (1.244121056 * x) ^ 4 must be equal to (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1.244121056 * x) ^ 4 is equal to 2.3958 * x^4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x) is equal to 2.3958 * x^4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this confirms that the geometric mean has been calculated correctly according to the instructions provided by the referenced website.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );