document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930689>Question 930689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the smallest natural number that is simultaneously the sum of 9, 10 and 11<BR>\n" );
document.write( "consecutive integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837440 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=837440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor has nothing to do with the given problem....<br><BR>\n" );
document.write( "Let the three strings of consecutive integers be<br><BR>\n" );
document.write( "a(1), ..., a(9)<BR>\n" );
document.write( "b(1), ..., b(10)<BR>\n" );
document.write( "c(1), ..., c(11)<br><BR>\n" );
document.write( "The sum of the each sequence is the number of terms in the sequence, multiplied by the average of the first and last terms.<br><BR>\n" );
document.write( "First sequence...<BR>\n" );
document.write( "The average of 9 consecutive integers is an integer;<BR>\n" );
document.write( "The sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28%28a%281%29%2Ba%289%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"9%28%28a%281%29%2Ba%289%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Second sequence...<BR>\n" );
document.write( "The average of 10 consecutive integers is not an integer, but the sum of the first and last integers is an integer;<BR>\n" );
document.write( "The sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28%28b%281%29%2Bb%2810%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"10%28%28b%281%29%2Bb%2810%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28b%281%29%2Bb%2810%29%29 ALIGN=MIDDLE  ALT=\"5%28b%281%29%2Bb%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Third sequence...<BR>\n" );
document.write( "The average of 11 consecutive integers is an integer;<BR>\n" );
document.write( "The sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%28%28c%281%29%2Bc%2811%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"11%28%28c%281%29%2Bc%2811%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The three sums are to be the same; that means the sum must be a multiple of 9, 5, and 11.  The least common multiple of 9, 5, and 11 is 495; and that is the answer to the problem.<br><BR>\n" );
document.write( "First sequence: 495 = 9(55) = 51+52+...+58+59<BR>\n" );
document.write( "Second sequence: 495 = 10(49.5) = 5(99) = 45+46+...+53+54<BR>\n" );
document.write( "Third sequence: 495 = 11(45) = 40+41+...+49+50<br><BR>\n" );
document.write( "ANSWER: 495<br><BR>\n" );
document.write( " </SPAN>\n" );
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