document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197256>Question 1197256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 10th term of the sequence -37,-34,-41 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830471 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=830471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "As the response from tutor @ikleyn says, the problem is nonsense; there is no way to know what the subsequent terms of the sequence are.  ANY following numbers make a valid sequence.<br><BR>\n" );
document.write( "Tutor @MathLover1 assumes the sequence is quadratic and obtains a solution.  It is true that, given a sequence of 3 terms, there is a unique polynomial function of degree 2 for which f(1), f(2), and f(3) are the three given numbers.<br><BR>\n" );
document.write( "But the problem does not say that the sequence is quadratic; it is bad mathematics to assume it is.  Furthermore, there are an infinite number of polynomials of degree greater than 2 which produce the given first three numbers.<br><BR>\n" );
document.write( "A third \"obvious\" pattern is that the sequence of differences \"plus 3, minus 7\" repeats, giving the sequence<br><BR>\n" );
document.write( "-37, -34, -41, -38, -45, -42, -49, -46, -53, -50<br><BR>\n" );
document.write( "In that sequence, the \"obvious\" 10th term is -50.<br><BR>\n" );
document.write( "So go with the answer from tutor @ikleyn: The problem as posed is nonsense.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );