document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=898852>Question 898852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question: In the gp, the sum of the 2nd and 3rd terms is 9. The 7th is 8 times the 4th. Find the first term, the ratio and the 5th term. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #545022 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=545022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given that:\r<BR>\n" );
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document.write( "the sum of the 2d and 3d terms is 9.\r<BR>\n" );
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document.write( "the 7th term is 8 times the 4th.\r<BR>\n" );
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document.write( "in a geometric progression, the formula for An is:\r<BR>\n" );
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document.write( "An = A1 * r^(n-1)\r<BR>\n" );
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document.write( "This means that A7 = A1 * r^6\r<BR>\n" );
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document.write( "This means that A4 = A1 * r^3\r<BR>\n" );
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document.write( "if A7 is 8 * A4, this means that:\r<BR>\n" );
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document.write( "A1 * r^6 = 8 * A1 * r^3\r<BR>\n" );
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document.write( "divide both sides of this equation by A1 * r^3 and you get:\r<BR>\n" );
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document.write( "(A1 * r^6) / (A1 * r^3) = 3\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "r^3 = 8 which results in r = 2.\r<BR>\n" );
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document.write( "you know  that A2 = A1 * r\r<BR>\n" );
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document.write( "you also know that A3 = A1 * r^2\r<BR>\n" );
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document.write( "since r = 2, this becomes:\r<BR>\n" );
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document.write( "A2 = A1 * 2\r<BR>\n" );
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document.write( "A3 = A1 * 4\r<BR>\n" );
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document.write( "the sum of A2 and A3 is equal to 6 * A1 which is equal to 9\r<BR>\n" );
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document.write( "this means that A1 must be equal to 3/2\r<BR>\n" );
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document.write( "since A1 is equal to 3/2 and r is equal to 2, this means that A5 is equal to A1 * r^4 which is equal to 3/2 * 2^4) which is equal to 3/2 * 16 which is equal to 24.\r<BR>\n" );
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document.write( "the progression from A1 to A7 is as follows:\r<BR>\n" );
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document.write( "A1 = 3/2<BR>\n" );
document.write( "A2 = 3/2 * 2 = 3<BR>\n" );
document.write( "A3 = 3/2 * 4 = 6<BR>\n" );
document.write( "A4 = 3/2 * 8 = 12<BR>\n" );
document.write( "A5 = 3/2 * 16 = 24<BR>\n" );
document.write( "A6 = 3/2 * 32 = 48<BR>\n" );
document.write( "A7 = 3/2 * 64 = 96\r<BR>\n" );
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document.write( "the sum of the second and third term is equal to 9 because 3 + 6 = 9<BR>\n" );
document.write( "the 7th term is 8 times the 4th term because 8 * 12 = 96\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "first term is equal to 3/2<BR>\n" );
document.write( "ratio is equal to 2<BR>\n" );
document.write( "fifth term is equal to 24.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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