document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163948>Question 1163948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: The sum of the first two terms of a decreasing geometric series is 5/4, and the sum to infinity is 9/4. Write the first three terms of the geometric series.\r<BR>\n" );
document.write( "\n" );
document.write( "I solved it. I dont need the answer. It was tedious, which is ok if that is the way to do it. But I need to know whether I am making it tedious because the way I approached it and whether I am missing another easier way to solve it! \r<BR>\n" );
document.write( "\n" );
document.write( "The way I solved it was: <BR>\n" );
document.write( "a + ar = 5/4   (1)<BR>\n" );
document.write( "a/(1-r) = 9/4  (2)\r<BR>\n" );
document.write( "\n" );
document.write( "Subtracting (1) - (2) gave me ar^2 (the third term) = 3/2 <BR>\n" );
document.write( "Dividing (1)/(2) gave me r= +/- (2/3) and in turn plugging the values gave me a=3/4.<BR>\n" );
document.write( "(Then I realized that there was no need for the tedious subtraction!!)\r<BR>\n" );
document.write( "\n" );
document.write( "Also can I assume 'dividing the sum of a geometric series by its sum to infinity will always yield r^2 '\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788207 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\">th partial sum of a geometric sequence is given by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{a\(1\,-\,r^n\)}{\(1\,-\,r\)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then, given that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large |r|\,<\,1\">, dividing the partial sum by the infinite sum:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=0}^\infty\ ar^i\ =\ \frac{a}{1\,-\,r}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "yields\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ r^n\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Which is consistent with your calculations, that is you got <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1\,-\,r^2\ =\ \frac{5}{9}\"> from which you got <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ =\ \pm\frac{2}{3}\"> using the partial sum <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large S_2\">.\r<BR>\n" );
document.write( "\n" );
document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );