document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132827>Question 1132827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 20th term of the AP: 80, 75, 70,…and calculate the number of terms required to make the sum equal to zero </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749958 by </B><A HREF=/tutors/aboutme.mpl?userid=Alex.33><B>Alex.33(110)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alex.33><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=Alex.33><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have<BR>\n" );
document.write( "1.It is arithmetic sequence<BR>\n" );
document.write( "2.the first 3 terms 80, 75, 70<BR>\n" );
document.write( "We want<BR>\n" );
document.write( "1.the 20th term<BR>\n" );
document.write( "2.the number n, for which the sum of the sequence S(n)=0<BR>\n" );
document.write( "Approach: <BR>\n" );
document.write( "1.the general formula of the nth term: a(n)<BR>\n" );
document.write( "2.plug n=20 in=>1.<BR>\n" );
document.write( "3.the general formula for the sum of the first n terms: S(n)<BR>\n" );
document.write( "4.set S(n)=0 and solve.\r<BR>\n" );
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document.write( "the common difference: -5<BR>\n" );
document.write( "the first term: 80<BR>\n" );
document.write( "a(n)=80+(-5)*(n-1)=85-5n\r<BR>\n" );
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document.write( "a(20)=-15=>the twelfth term\r<BR>\n" );
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document.write( "S(n)=(80+a(n))*n/2=0<BR>\n" );
document.write( "n=33=>the number of terms required to make the sum equal to zero </SPAN>\n" );
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