document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209375>Question 1209375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence.  If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848707 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=848707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Since the sequence a_1, a_2, a_3, ..., a_10 is arithmetic, the sequences<br><BR>\n" );
document.write( "[1] a_1, a_3, a_5<br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "[2] a_2, a_4<br><BR>\n" );
document.write( "are also both arithmetic.<br><BR>\n" );
document.write( "In [1], a_3 is the middle term of the three, so it is the average of the three terms; since a_1 + a_3 + a_5 = 5, a_3 must be 5/3.<br><BR>\n" );
document.write( "But in [2], a_3 is halfway between a_2 and a_4, so a_3 must be the average of a_2 and a_4.  And a_2 + a_4 = -2, which means a_3 must be -2/2 = -1.<br><BR>\n" );
document.write( "So the conditions of the problem require that a_3 be both 5/3 and -1, which is a contradiction.<br><BR>\n" );
document.write( "ANSWER: The problem is faulty<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );