document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023578>Question 1023578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the smallest positive term of the progression 100, 97, 94...(Don't enumerate) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #639079 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=639079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i would find the number of terms required for the sum to be 0.<BR>\n" );
document.write( "it will either be an integer, or it will not.<BR>\n" );
document.write( "the answer will be 1 less than the number of terms indicated.\r<BR>\n" );
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document.write( "let's see if this works.\r<BR>\n" );
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document.write( "the general formula is An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "since is equal to -3, and A1 is equal to 100, then the formula becomes An = 100 + (n-1) * -3.\r<BR>\n" );
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document.write( "simplify this to get An = 100 - 3 * (n-1).\r<BR>\n" );
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document.write( "simplify further to get An = 100 - 3n + 3.\r<BR>\n" );
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document.write( "simplify further to get An = 103 - 3n.\r<BR>\n" );
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document.write( "set An equal to 0 and this becomes 0 = 103 - 3n.\r<BR>\n" );
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document.write( "add 3n to both sides of this equation and you get 3n = 103.\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get n = 103 / 3 = 34.333.....\r<BR>\n" );
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document.write( "take the lower figure and you get n = 34.\r<BR>\n" );
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document.write( "your answer should be that the smallest positive will be when n = 34.\r<BR>\n" );
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document.write( "when n = 34, the formula becomes An = 103 - 3 * 34 which is equal to 1.\r<BR>\n" );
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document.write( "when n = 35, the formula becomes An = 103 - 3 * 35 which is equal to -2.\r<BR>\n" );
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document.write( "looks like n = 34 gets you the least positive value which is 1.\r<BR>\n" );
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document.write( "sticking to the original formula, you would get:\r<BR>\n" );
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document.write( "An = 100 + (n-1) * -3 becomes An = 100 -3 * (n-1) which becomes A34 = 100 - 3 * 33 which becomes A34 = 100 - 99 which becomes A34 = 1.\r<BR>\n" );
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document.write( "the solution is confirmed.\r<BR>\n" );
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document.write( "the least positive value you can get is 1.\r<BR>\n" );
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