document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140751>Question 1140751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bonus: The number 15 is the smallest positive number which is a sum of two consecutive numbers, three consecutive numbers, and five consecutive numbers:<BR>\n" );
document.write( "15 = 7+8<BR>\n" );
document.write( "15 = 4+5+6<BR>\n" );
document.write( "15 = 1+2+3+4+5<BR>\n" );
document.write( "What is the largest number under 1000 that satisfies the same conditions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761253 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=761253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) The sum of 3 consecutive numbers is 3 times the number in the middle; the sum of 5 consecutive numbers is 5 times the number in the middle.  So any number that can be written as the sum of both 3 consecutive numbers and 5 consecutive numbers must be a multiple of both 3 and 5, and therefore must be a multiple of 15.<br><BR>\n" );
document.write( "(2) The sum of 2 consecutive numbers is always odd.<br><BR>\n" );
document.write( "(3) From (1) and (2), the numbers that can be written as the sum of 2, 3, or 5 consecutive numbers are all the odd multiples of 15.<br><BR>\n" );
document.write( "(4) The largest odd multiple of 15 less than 1000 is 975.<br><BR>\n" );
document.write( "ANSWER: 975 </SPAN>\n" );
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