document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205056>Question 205056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many terms of the arithmetic sequence 2, 4, 6, 8, ... add up to 60,762?  Can anyone help me with the answer and how you solved for it?  I am confused and have gotten several different answers trying to do this problem.  Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154789 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there is a \"canned\" formula; but if you look at what's going on, it is pretty straightforward\r<BR>\n" );
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document.write( "the difference between consecutive terms in this sequence is 2\r<BR>\n" );
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document.write( "the first term is 2\r<BR>\n" );
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document.write( "let X be the number of terms it takes to sum to 60762\r<BR>\n" );
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document.write( "the value of the nth term is 2n\r<BR>\n" );
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document.write( "the sum of the 1st and last terms is 2 + 2X<BR>\n" );
document.write( "the sum of the 2nd and next to last terms is 4 + (2X-2) or 2X + 2<BR>\n" );
document.write( "the sum of the 3rd and second to last trems is 6 + (2X-4) or 2X + 2<BR>\n" );
document.write( "this pattern is consistent<BR>\n" );
document.write( "the number of pairs is HALF the number of terms\r<BR>\n" );
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document.write( "so the sum of X terms of the sequence is (2X + 2)(X / 2) or X^2 + X\r<BR>\n" );
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document.write( "X^2 + X = 60762 ___ X (X + 1) = 60762 \r<BR>\n" );
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document.write( "so you are looking for two factors of 60762 that are one number apart<BR>\n" );
document.write( "___ the values are close to the square root of 60762<BR>\n" );
document.write( "___ 246 and 247\r<BR>\n" );
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document.write( "246 terms  </SPAN>\n" );
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