document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185522>Question 1185522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the missing term in harmonic sequence. Show the solution\r<BR>\n" );
document.write( "\n" );
document.write( "___,1/2,2/5,1/3,___ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817064 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from tutor @robertb shows one way of solving a problem like this involving harmonic sequences.<br><BR>\n" );
document.write( "Here is a different way that I personally prefer.<br><BR>\n" );
document.write( "In a harmonic sequence, the terms can be written with a common NUMERATOR, and with DENOMINATORS that form an arithmetic sequence.<br><BR>\n" );
document.write( "So given the harmonic sequence<br><BR>\n" );
document.write( "____, 1/2, 2/5, 1/3, ____<br><BR>\n" );
document.write( "rewrite all the given terms with the same numerator:<br><BR>\n" );
document.write( "____, 2/4, 2/5, 2/6, ____<br><BR>\n" );
document.write( "Then the pattern is clear:<br><BR>\n" );
document.write( "2/3, 2/4, 2/5, 2/6, 2/7<br><BR>\n" );
document.write( "ANSWER: The missing numbers are 2/3 and 2/7<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );