document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027966>Question 1027966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first three terms of a geometric sequence are: T1 ; T2 ; and T3. If T2 = T1 + 4 and T3= T2 + 9, determine the values of T1; T2 and T3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643148 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=643148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i got an answer, but the numbers involved are not integers.\r<BR>\n" );
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document.write( "here's what i did.\r<BR>\n" );
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document.write( "T1 = x<BR>\n" );
document.write( "T2 = T1 + 4 = x + 4<BR>\n" );
document.write( "T3 = T2 + 9 = (T1 + 4) + 9 = T1 + 13 = x + 13\r<BR>\n" );
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document.write( "your 3 numbers are:\r<BR>\n" );
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document.write( "x<BR>\n" );
document.write( "x + 4<BR>\n" );
document.write( "x + 13\r<BR>\n" );
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document.write( "you state it's a geometric sequence which means An = A1 * r^(n-1)\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "A1 = A1 * r^(1-1) = A1 * r^0 = A1 * 1 = A1 = x\r<BR>\n" );
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document.write( "A2 = A1 * r^(2-1) = A1 * r^1 = A1 * r = x * r\r<BR>\n" );
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document.write( "A3 = A1 * r^(3-1) = A1 * r^2 = x * r^2\r<BR>\n" );
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document.write( "you wind up with:\r<BR>\n" );
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document.write( "A1 = x<BR>\n" );
document.write( "A2 = x * r<BR>\n" );
document.write( "A3 = x * r^2\r<BR>\n" );
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document.write( "A2 is the second term in the sequence which you already know is equal to x + 4\r<BR>\n" );
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document.write( "this means that x+4 = x*r\r<BR>\n" );
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document.write( "you can solve for r to get r = (x+4)/x\r<BR>\n" );
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document.write( "A3 is the third term in the sequence which you already know is equal to x + 13\r<BR>\n" );
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document.write( "this means that x+13 = x*r^2\r<BR>\n" );
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document.write( "you can solve for r^2 to get r^2 = (x+13)/x\r<BR>\n" );
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document.write( "if r = (x+4)/x, then r^2 must be equal to ((x+4)/x)^2 which is equal to (x+4)^2 / x^2\r<BR>\n" );
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document.write( "you now have r^2 = (x+4)^2 / x^2 and you have r^2 = (x+13)/x\r<BR>\n" );
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document.write( "this means that (x+4)^2 / x^2 = (x+13) / x\r<BR>\n" );
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document.write( "multiply both sides of this equation by x^2 and you get:\r<BR>\n" );
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document.write( "(x+4)^2 = (x+13) * x\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "x^2 + 8x + 16 = x^2 + 13x\r<BR>\n" );
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document.write( "subtract x^2 from both sides of the equation and subtract 8x from both sides of the equation and you get:\r<BR>\n" );
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document.write( "16 = 5x\r<BR>\n" );
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document.write( "solve for x to get x = 16/5\r<BR>\n" );
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document.write( "you know that r = (x+4)/x\r<BR>\n" );
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document.write( "when x = 16/5, this becomes:\r<BR>\n" );
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document.write( "r = (16/5 + 4) / (16/5)\r<BR>\n" );
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document.write( "since 4 is equal to 20/5, this equation becomes:\r<BR>\n" );
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document.write( "r = (16/5 + 20/5) / (16/5)\r<BR>\n" );
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document.write( "simplify to get r = (36/5) / (16/5)\r<BR>\n" );
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document.write( "this is the same as r = (36/5) * (5/16) which results in r = 36/16 which simplies to r = 9/4\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 16/5<BR>\n" );
document.write( "r = 9/4\r<BR>\n" );
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document.write( "you were given that:\r<BR>\n" );
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document.write( "A1 = x<BR>\n" );
document.write( "A2 = x+4<BR>\n" );
document.write( "A3 = x+13\r<BR>\n" );
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document.write( "when x = 16/5, this becomes:\r<BR>\n" );
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document.write( "A1 = 16/5<BR>\n" );
document.write( "A2 = 16/5 + 4 = 16/5 + 20/5 = 36/5<BR>\n" );
document.write( "A3 = 16/5 + 13 = 16/5 + 65/5 = 81/5\r<BR>\n" );
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document.write( "you are also given that:\r<BR>\n" );
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document.write( "A1 = x * r^0<BR>\n" );
document.write( "A2 = x * r^1<BR>\n" );
document.write( "A3 = x * r^2\r<BR>\n" );
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document.write( "when x = 16/5 and r = 9/4, this becomes:\r<BR>\n" );
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document.write( "A1 = 16/5 * (9/4)^0 = 16/5 * 1 = 16/5<BR>\n" );
document.write( "A2 = 16/5 * (9/4)^1 = 16/5 * 9/4 = 144/20 = 36/5<BR>\n" );
document.write( "A3 = 16/5 * (9/4)^2 = 16/5 * 81/16 = 1296/80 = 81/5\r<BR>\n" );
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document.write( "the geometric formula yields the same answer when x = 16/5 and when r = 9/4.\r<BR>\n" );
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document.write( "you were asked to determine the value of T1 and T2 and T3.\r<BR>\n" );
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document.write( "those values are:\r<BR>\n" );
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document.write( "16/5<BR>\n" );
document.write( "36/5<BR>\n" );
document.write( "81/5\r<BR>\n" );
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document.write( "you were given that T2 = T1 + 4\r<BR>\n" );
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document.write( "that would make T2 = 16/5 + 4 = 16/5 + 20/5 = 36/5\r<BR>\n" );
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document.write( "you were given that T3 = T2 + 9\r<BR>\n" );
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document.write( "that would make T3 = 36/5 + 9 = 36/5 + 45/5 = 81/5\r<BR>\n" );
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document.write( "looks like we're good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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