document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210224>Question 1210224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of sequences containing three terms, such that<BR>\n" );
document.write( "* The second term is equal to the sum of the first term plus one.\r<BR>\n" );
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document.write( "* The third term is equal to twice the second term.<BR>\n" );
document.write( "* Each term is an integer in \{0, 1, 2, \dots, 100\}.<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 #851693 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=851693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "According to the definition of the sequence, each sequence is of the form<br><BR>\n" );
document.write( "n, n+1, 2n+2<br><BR>\n" );
document.write( "The numbers that can be used are the integers from 0 to 100, inclusive.  So the \"last\" sequence is the one in which 2n+2 is equal to 100.<br><BR>\n" );
document.write( "2n+2 = 100<BR>\n" );
document.write( "2n = 98<BR>\n" );
document.write( "n = 49<br><BR>\n" );
document.write( "The \"first\" sequence is clearly the one in which n is 0.<br><BR>\n" );
document.write( "So the sequences that satisfy the conditions of the problem are those where n is from 0 to 49, inclusive, which means 50 such sequences.<br><BR>\n" );
document.write( "ANSWER: 50<br><BR>\n" );
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