document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843435>Question 843435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My problem is to find the indicated term for the geometric series described : \r<BR>\n" );
document.write( "\n" );
document.write( "Sn=33 an=48 r=-2 , find a1. \r<BR>\n" );
document.write( "\n" );
document.write( "I am trying to use the formula SN= a1-a1 r(n)/ 1-r <BR>\n" );
document.write( "However, i am missing 2 variables both a1 and \"n\".  I have tried to solve first using an=a1 r (n-1) but again, i am missing 2 variables (a1 and n). \r<BR>\n" );
document.write( "\n" );
document.write( "Please tell me how to solve for a1. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508227 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=508227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sn = 33<BR>\n" );
document.write( "An = 48<BR>\n" );
document.write( "R = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The formula for the Last term of a geometric series is An = A1 * (R)^(n-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The formula for the sum of a geometric series is Sn = A1 * (1 - r^n) / (1 - r)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I was actually able to find A1 and n but it wasn't easy.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I got n = .60768258\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once I got n, I was able to find A1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I got A1 = 63\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your answer is A1 = 63.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I tried to solve it by formula but wound up in a dead end because I was getting logs of a negative number which is not allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solving simultaneous equations by graphing is a legitimate solution technique.<BR>\n" );
document.write( "I'm not sure if I should have been able to solve it by formula, but I couldn't do it, so graphing was the only other way I knew how to find it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What I did was solve for A1 in both equations and then set those equations equal to each other.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I then subtracted the second equation from the first and graphed it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "My solution was where the graph crosses the x-axis.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The two equations that I subtracted from each other are equal at that point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once I found the value of n, I was able to substitute for n in either equation to get A1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's the details of what I did.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An = A1 * (2^(n-1))<BR>\n" );
document.write( "Solve for A1 to get A1 = An / (2^(n-1))<BR>\n" );
document.write( "Replace An with 48 to get A1 = 48 / (2^(n-1))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The second equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sn = A1 * (1 - 2^n) / (1 - 2)<BR>\n" );
document.write( "Simplify to get:<BR>\n" );
document.write( "Sn = A1 * (1 - 2^n) / (-1)<BR>\n" );
document.write( "Simplify further to get:<BR>\n" );
document.write( "Sn = (-A1) * (1 - 2^n)<BR>\n" );
document.write( "Replace Sn with 33 to get:<BR>\n" );
document.write( "33 = (-A1) * (1 - 2^n)<BR>\n" );
document.write( "divide both sides of this equation by (1 - 2^n) to get:<BR>\n" );
document.write( "33 / (1 - 2^n) = -A1<BR>\n" );
document.write( "multiply both sides of this equation by -1 to get:<BR>\n" );
document.write( "-33 / (1 - 2^n) = A1<BR>\n" );
document.write( "commute this equation (flip sides) to get:<BR>\n" );
document.write( "A1 = -33 / (1 - 2^n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The equations that I got for A1 are:<BR>\n" );
document.write( "A1 = 48 / 2^(n-1)<BR>\n" );
document.write( "and:<BR>\n" );
document.write( "A1 = -33 / (1 - 2^n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since both expressions on the right side of these equations are equal to A1, I set the expressions on the right side of each equation equal to each other to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "48 / 2^(n-1) = -33 / (1 - 2^n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I tried to solve this using logs but wound up with logs of a negative number which isn't allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's when I resorted to graphing.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I added the right side of the equation to both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "48 / 2^(n-1) + 33 / (1 - 2^n) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I then set this equation equal to y and graphed it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The equation that was graphed is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 48 / (2^(x-1)) + 33 / (1 - 2^x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I had to change n to x in order for the graphing software to work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of that equation is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C3%2C-100%2C100%2C48+%2F+%282%5E%28x-1%29%29+%2B+33+%2F+%281+-+2%5Ex%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can't really get the value from the graph.<BR>\n" );
document.write( "I used the TI-84 which tells you what the zero crossing point is.<BR>\n" );
document.write( "I then use the same TI-84 to find A1 which it told me was 63.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The value of A1 = 63 was generated using the internally stored value of n rather than the rounded value of n that is shown above.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The actual zero crossing shown on my TI-84 was x = .60768258.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's the value of n.   It doesn't look rounded but it is.   The internally stored number carries it out to more decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use that value and you get A1 = something close to 63, but not 63.<BR>\n" );
document.write( "When I used the internally stored number from the TI-84 I got 63 exactly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Anyway, the problem is solved.<BR>\n" );
document.write( "A1 = 63\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The method to find the solution was graphing of the equations that were used to solve for A1 in terms of n.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );