document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199329>Question 1199329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The increasing sequence T = 2 3 5 6 7 8 10 11 consists of all positive integers which are not perfect squares. What is the 2012th term of T?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833160 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=833160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "2012 is a bit less than 45^2 = 2025, so there are 44 perfect squares less than 2012.<br><BR>\n" );
document.write( "2012-44 = 1968, so the number 2012 is the 1968-th term in the sequence.<br><BR>\n" );
document.write( "To find the 2012-th term, we need to add 44 more terms, which means adding 44 to 2012, to get 2056.  But one of the numbers between 2012 and 2056 is another perfect square, so we need to go one number farther, to 2057.<br><BR>\n" );
document.write( "ANSWER: the 2012-th term in the sequence is 2057.<br><BR>\n" );
document.write( "There are of course different paths of logical reasoning to arrive at the answer....<br><BR>\n" );
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