document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427328>Question 427328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the sum of the multiples of 3 from 3 to 99 inclusive </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297188 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=297188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the multiples of 3 are 3,6,9,12,15,18,21,24,27,30,......... all the way up to 99.\r<BR>\n" );
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document.write( "this is an arithmetic series with a common difference of 3.\r<BR>\n" );
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document.write( "the formula for the sum of an arithmetic series is:\r<BR>\n" );
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document.write( "Sn = (n/2) * (a1 + an)\r<BR>\n" );
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document.write( "Sn = the sum of the n terms in the sequence.<BR>\n" );
document.write( "a1 = the first term in the sequence.<BR>\n" );
document.write( "an = the nth term in the sequence.\r<BR>\n" );
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document.write( "our first term is 3 and our last term is 99.\r<BR>\n" );
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document.write( "the common difference is 3.\r<BR>\n" );
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document.write( "to find the number of terms, we take the last term and divide it by 3 to get 33.\r<BR>\n" );
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document.write( "there are 33 terms in the sequence, so n = 33\r<BR>\n" );
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document.write( "our formula becomes Sn = (33/2 * (3 + 99) which becomes (33/2) * 102 which becomes 33 * 51 which becomes 1683.\r<BR>\n" );
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document.write( "to see how this works, we can use smaller numbers.\r<BR>\n" );
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document.write( "assume the first term is 3 and the last term is 9.\r<BR>\n" );
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document.write( "the common difference is 3.\r<BR>\n" );
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document.write( "the number of terms is 9/3 = 3\r<BR>\n" );
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document.write( "the formula states that Sn = (3/2) * (3 + 9) = (3/2) * (12) = 3*6 = 18\r<BR>\n" );
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document.write( "if we sum up the terms in the sequence we should equal 18.\r<BR>\n" );
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document.write( "3 + 6 + 9 = 9 + 9 = 18.\r<BR>\n" );
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document.write( "the formula works.\r<BR>\n" );
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document.write( "same thing happens with the larger numbers only it's much harder to show you because there's so many more numbers to add up.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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