document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=236340>Question 236340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the smallest integer that could be part of a set of two or more positive consecutive integers whose sum is 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 #173988 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=173988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe the number is 9\r<BR>\n" );
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document.write( "9 sum 9<BR>\n" );
document.write( "10 sum 19<BR>\n" );
document.write( "11 sum 30<BR>\n" );
document.write( "12 sum 42<BR>\n" );
document.write( "13 sum 55<BR>\n" );
document.write( "14 sum 69<BR>\n" );
document.write( "15 sum 84<BR>\n" );
document.write( "16 sum 100\r<BR>\n" );
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document.write( "I summed the numbers from 1 up to when i got past 100.\r<BR>\n" );
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document.write( "I then looked at each number over 100 to see if there were sums in the lower range of numbers that I could subtract to get 100.\r<BR>\n" );
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document.write( "When I got to the sum of the number at 16 was 136, I saw that the sum of the numbers at 8 totaled 36 so I could subtract the first 8 numbers from the set and my total from 9 to 16 would equal 100.\r<BR>\n" );
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document.write( "It worked although I don't have a formula to apply to it.\r<BR>\n" );
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document.write( "The formula for the sum of an arithmetic progression can be applied.\r<BR>\n" );
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document.write( "It is:\r<BR>\n" );
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document.write( "S = n*(x+y)/2 where\r<BR>\n" );
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document.write( "x = first number in the sequence<BR>\n" );
document.write( "y = last number in the sequence.\r<BR>\n" );
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document.write( "For this progression, we have:\r<BR>\n" );
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document.write( "n = 8<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "y = 16\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "S = 8*(9+16)/2 which becomes:\r<BR>\n" );
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document.write( "S = 8*25/2 = 100\r<BR>\n" );
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document.write( "Our solution became:\r<BR>\n" );
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document.write( "S = 16*(1+16)/2 - 8*(1+8)/2 which became:\r<BR>\n" );
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document.write( "S = 8*17 - 4*9 = 136 - 36 = 100\r<BR>\n" );
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document.write( "I suspect there's a generic formula in there to help solve this problem a little more rigorously using algebra, but I don't have that answer for you.\r<BR>\n" );
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document.write( "The answer, however, is correct as best as I can determine, and it is:\r<BR>\n" );
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document.write( "The smallest number in a consecutive series that adds up to 100 is 9.\r<BR>\n" );
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document.write( "The number of numbers involved is 8.\r<BR>\n" );
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