document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132426>Question 1132426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the first five terms of the arithmetic series in which the sum of the second and ninth terms is 25, and the sum of the third and seventh terms is 20. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749493 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=749493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for the nth term of an arithmetic sequence is<BR>\n" );
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document.write( "x(n) = a +d(n-1), where a is the first term, d is the common difference<BR>\n" );
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document.write( "x(2) = a +d(2-1) = a +d<BR>\n" );
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document.write( "x(9) = a +d(9-1) = a +8d<BR>\n" );
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document.write( "x(2)+x(9) = 25 = a +d +a +8d = 2a +9d<BR>\n" );
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document.write( "1) 2a +9d = 25<BR>\n" );
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document.write( "x(3) = a +d(3-1) = a +2d<BR>\n" );
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document.write( "x(7) = a +d(7-1) = a +6d<BR>\n" );
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document.write( "x(3) +x(7) = 20 = a +2d +a +6d = 2a +8d<BR>\n" );
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document.write( "2a +8d = 20<BR>\n" );
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document.write( "2) a +4d = 10<BR>\n" );
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document.write( "solve equation 2 for a<BR>\n" );
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document.write( "a = 10-4d<BR>\n" );
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document.write( "substitute for a in equation 1<BR>\n" );
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document.write( "2(10-4d) +9d = 25<BR>\n" );
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document.write( "20 -8d +9d = 25<BR>\n" );
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document.write( "d = 5<BR>\n" );
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document.write( "a = 10-4(5) = 10 -20 = -10<BR>\n" );
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document.write( "the first five terms are -10, -5, 0, 5, 10<BR>\n" );
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document.write( "Note<BR>\n" );
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document.write( "x(1) = a +d(1-1) = a = -10<BR>\n" );
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document.write( "x(2) = a +d(2-1) = a +d = -10 +5 = -5<BR>\n" );
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document.write( "x(3) = a +d(3-1) = a +2d = -10 +5(2) = 0<BR>\n" );
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document.write( "X(4) = a +d(4-1) = a +3d = -10 +5(3) = 5<BR>\n" );
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document.write( "x(5) = a +d(5-1) = a +4d = -10 +5(4) = 10<BR>\n" );
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document.write( "check answers<BR>\n" );
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document.write( "x(9) = a +8d = -10 +8(5) = 30<BR>\n" );
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document.write( "x(2) +x(9) = -5 +30 = 25<BR>\n" );
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document.write( "x(7) = a +6d = -10 +6(5) = 20<BR>\n" );
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document.write( "x(3) +x(7) = 0 +20 = 20<BR>\n" );
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document.write( "answer checks<BR>\n" );
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