document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1069078>Question 1069078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the 5th term of an arithmetic sequence is 0 and the 13th term is equal to 12. Using suitable formulae determine the common difference,the first term,and the sum of the first 21 terms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #684304 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=684304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form for the nth term of an arithmetic sequence is<BR>\n" );
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document.write( "a(n) = a(1) + d(n-1), where d is the common difference<BR>\n" );
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document.write( "we have two equations in two unknowns<BR>\n" );
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document.write( "1) a(5) = a(1) + d(5-1) = a(1) + 4d = 0<BR>\n" );
document.write( "2) a(13) = a(1) + d(13-1) = a(1) + 12d = 12<BR>\n" );
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document.write( "solve equation 1) for a(1) and substitute for a(1) in equation 2<BR>\n" );
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document.write( "-4d + 12d = 12<BR>\n" );
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document.write( "d = 12/8 = 3/2<BR>\n" );
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document.write( "substitute for d in equation 1<BR>\n" );
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document.write( "a(1) + 4(3/2) = 0<BR>\n" );
document.write( "a(1) = -6<BR>\n" );
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document.write( "check our answers, that is, d = 3/2 and a(1) = -6<BR>\n" );
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document.write( "equation 1<BR>\n" );
document.write( "-6 + 4(3/2) = 0<BR>\n" );
document.write( "0 = 0<BR>\n" );
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document.write( "equation 2<BR>\n" );
document.write( "-6 +12(3/2) = 12<BR>\n" );
document.write( "12 = 12<BR>\n" );
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document.write( "our answers for d and a(1) check<BR>\n" );
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document.write( "the sum of the first n terms of an arithmetic sequence is<BR>\n" );
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document.write( "S(n) = (1/2) * n * ( a(1) + a(n) )<BR>\n" );
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document.write( "we are asked for s(21)<BR>\n" );
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document.write( "note that a(21) = -6 + (3/2) * (21 - 1) = 24<BR>\n" );
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document.write( "S(21) = (1/2) * 21 * (-6 + 24) = 189<BR>\n" );
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