document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=961982>Question 961982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please can you help me with this. I've been trying but I can't seem to solve it.\r<BR>\n" );
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document.write( "If the sum of the 8th and 9th terms of an a.p is 72 and the 4th term is -6, find the common difference.\r<BR>\n" );
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document.write( "Thank you so much in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587722 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=587722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is an interesting problem.<BR>\n" );
document.write( "i solve it this way.\r<BR>\n" );
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document.write( "the general equation is An = A1 + (n-1)*d\r<BR>\n" );
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document.write( "from this you get:\r<BR>\n" );
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document.write( "A4 = A1 + 3d<BR>\n" );
document.write( "A8 = A1 + 7d<BR>\n" );
document.write( "A9 = A1 + 8d\r<BR>\n" );
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document.write( "you are given that A4 is equal to -6.<BR>\n" );
document.write( "from that you get:\r<BR>\n" );
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document.write( "-6 = A1 + 3d\r<BR>\n" );
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document.write( "you are given that the sum of A7 and A8 is equal to 72.<BR>\n" );
document.write( "from that you get:\r<BR>\n" );
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document.write( "72 = A1 + 7d + A1 + 8d<BR>\n" );
document.write( "combine like terms and you get:\r<BR>\n" );
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document.write( "72 = 2A1 + 15d\r<BR>\n" );
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document.write( "you now have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "-6 = A1 + 3d<BR>\n" );
document.write( "72 = 2A1 + 15d\r<BR>\n" );
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document.write( "multiply the first equation by 2 and you get:\r<BR>\n" );
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document.write( "-12 = 2A1 + 6d<BR>\n" );
document.write( "72 = 2A1 + 15d\r<BR>\n" );
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document.write( "subtract the first equation from the second equation and you get:\r<BR>\n" );
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document.write( "84 = 9d\r<BR>\n" );
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document.write( "solve for d and you get:\r<BR>\n" );
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document.write( "d = 9.333333333333333........ which is the same as (9 and 1/3).\r<BR>\n" );
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document.write( "that's your common difference.\r<BR>\n" );
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document.write( "you can confirm by using that value of d to solve for A1.<BR>\n" );
document.write( "you will get A1 = -34.\r<BR>\n" );
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document.write( "you can then use A1 and d to solve for A4 and A8 and A9\r<BR>\n" );
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document.write( "you will find that A4 will be equal to -6 and the sum of A8 and A9 will be equal to 72.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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