document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839227>Question 839227</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The sum of the first 4 terms of an arithmetic sequence is 24. The 7th term exceeds the 4th term by 24. Determine the sum of the first 12 terms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505628 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for the nth term in an arithmetic sequence is:<BR>\n" );
document.write( "Un = U1 + (n - 1)d<BR>\n" );
document.write( "in which Un is the nth term, U1 is the 1st term, and d is the difference.<BR>\n" );
document.write( "So, for the 2nd term: U2 = U1 + (2 - 1)d = U1 + d<BR>\n" );
document.write( "for the 3rd term: U3 = U1 + (3 - 1)d = U1 + 2d<BR>\n" );
document.write( "for the 4th term: U4 = U1 + (4 - 1)d = U1 + 3d<BR>\n" );
document.write( "and so on.\r<BR>\n" );
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document.write( "The sum of the first 4 terms of an arithmetic sequence is 24:<BR>\n" );
document.write( "U1 + U2 + U3 + U4 = 24<BR>\n" );
document.write( "U1 + (U1 + d) + (U1 + 2d) + (U1 + 3d) = 24<BR>\n" );
document.write( "4U1 + 6d = 24<BR>\n" );
document.write( "divide all by 2:<BR>\n" );
document.write( "2U1 + 3d = 12\r<BR>\n" );
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document.write( "The 7th term exceeds the 4th term by 24:<BR>\n" );
document.write( "7th term: U7 = U1 + (7 - 1)d = U1 + 6d<BR>\n" );
document.write( "U7 = U4 + 24<BR>\n" );
document.write( "U1 + 6d = U1 + 3d + 24<BR>\n" );
document.write( "U1 + 6d - U1 - 3d = 24<BR>\n" );
document.write( "6d = 3d + 24<BR>\n" );
document.write( "6d - 3d = 24<BR>\n" );
document.write( "3d = 24<BR>\n" );
document.write( "d = 24/3 = 8\r<BR>\n" );
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document.write( "2U1 + 3d = 12<BR>\n" );
document.write( "2U1 + 3(8) = 12<BR>\n" );
document.write( "2U1 + 24 = 12<BR>\n" );
document.write( "2U1 = -12<BR>\n" );
document.write( "U1 = 12/2 = -6\r<BR>\n" );
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document.write( "The sum of the first n term can be found by using this formula:<BR>\n" );
document.write( "Sn = n/2 * {2U1 + (n - 1)d}\r<BR>\n" );
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document.write( "so, the sum of the first 12 term is:<BR>\n" );
document.write( "S12 = 12/2 * {2(-6) + (12 - 1)8}<BR>\n" );
document.write( "S12 = 6 * (-12 + 11*8)<BR>\n" );
document.write( "S12 = 6 * (-12 + 88)<BR>\n" );
document.write( "S12 = 6 * 76<BR>\n" );
document.write( "S12 = 456 </SPAN>\n" );
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