document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108288>Question 1108288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi could you plz help me with this question:\r<BR>\n" );
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document.write( "For the arithmetic sequence with t7 = 0.6 and t12 = -0.4, find t20.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723307 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=723307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> T7 = .6<BR>\n" );
document.write( "T12 = -.4\r<BR>\n" );
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document.write( "T7 is the 7th term in the sequence.<BR>\n" );
document.write( "T12 is the 12th term in the sequence.\r<BR>\n" );
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document.write( "T12 - T7 = -.4 - .6 = -1<BR>\n" );
document.write( "12 - 7 = 5\r<BR>\n" );
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document.write( "the difference between each term in the sequence is therefore -1/5 = -.2\r<BR>\n" );
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document.write( "T20 = x<BR>\n" );
document.write( "T12 = -.4\r<BR>\n" );
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document.write( "we assign the variable x to T20 because we don't know what the value of T2  is just yet.\r<BR>\n" );
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document.write( "T20 is the 20th term in the sequence.<BR>\n" );
document.write( "T12 is the 12th term in the sequence\r<BR>\n" );
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document.write( "T20 - T12 = x - (-.4) = x + .4<BR>\n" );
document.write( "20 - 12 = 8\r<BR>\n" );
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document.write( "the common difference between each term is -.2<BR>\n" );
document.write( "the difference between T20 and T12 is x + .4<BR>\n" );
document.write( "the difference between term number 20 and term number 12 is 8.<BR>\n" );
document.write( "therefore -.2 = (x + .4) / 8<BR>\n" );
document.write( "multiply both sides of this equation by 8 to get:<BR>\n" );
document.write( "-1.6 = x + .4<BR>\n" );
document.write( "subtract .4 from both sides of this equation to get:<BR>\n" );
document.write( "-2 = x\r<BR>\n" );
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document.write( "the value of the 20th term is therefore -2.\r<BR>\n" );
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document.write( "since this is an arithmetic sequence, then there is a common difference between each term.\r<BR>\n" );
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document.write( "we found that common difference to be equal to -.2\r<BR>\n" );
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document.write( "once we found that, we could find the value of any term in the sequence from any term that we know the value of.\r<BR>\n" );
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document.write( "we know the value of the 12th term is -.4<BR>\n" );
document.write( "we know that the common difference between terms is -.2<BR>\n" );
document.write( "we know that there are 8 terms between the 12th term and the 20th term.<BR>\n" );
document.write( "the difference between the 12th term and the 20th term is therefore 8 * -.2 = -1.6<BR>\n" );
document.write( "we add -1.6 to -.4 and we get -2.\r<BR>\n" );
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document.write( "the solution to your problem is that the value of T20 is equal to -2.\r<BR>\n" );
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