document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935611>Question 935611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve the 2nd term of an exponantial sequence which is 9 while the 4th term is 81. Find the common ratio,the first term and the sum of the first five terms of the sequence.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568859 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=568859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for the exponential sequence is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An = A0 * B^n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An is the nth term in the sequence.<BR>\n" );
document.write( "A0 is the first term in the sequence<BR>\n" );
document.write( "B is the base that is being raised to the exponent.<BR>\n" );
document.write( "B is the common ratio.<BR>\n" );
document.write( "n is the number of the term in the sequence.<BR>\n" );
document.write( "n is also the exponent that B is being raised to.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the second term in the sequence, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A2 = A0 * B^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since A2 is equal to 9, the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9 = A0 * B^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the fourth term in the sequence, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A4 = A0 * B^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since A4 is equal to 81, the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "81 = A0 * B^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your 2 equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9 = A0 * B^2<BR>\n" );
document.write( "81 = A0 * B^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve each of these equations for A0 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A0 = 9 / B^2<BR>\n" );
document.write( "A0 = 81 / B^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by substituting 9 / B^2 for A0 from the first equation, your second equation  of A0 = 81 / B^4 becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9 / B^2 = 81 / B^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by B^4 and divide both sides of this equation by 9 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B^4 / B^2 = 81 / 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B^2 = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the square root of both sides of this equation and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B = plus or minus 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B can't be negative, so B has to be equal to 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the common ratio, which is B, is equal to 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also solve for A1 by replacing B with 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from the above equations for A0, you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A0 = 9 / B^2<BR>\n" );
document.write( "A0 = 81 / B^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace B with 3 and those equations becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A0 = 9 / 3^2 = 9 / 9 = 1<BR>\n" );
document.write( "A0 = 81 / 3^4 = 81 / 81 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A1 is equal to 1.<BR>\n" );
document.write( "B is equal to 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An is equal to 1 * 3^n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n is equal to 0, An is equal to 1 * 3^0 which is equal to 1<BR>\n" );
document.write( "when n is equal to 1, An is equal to 1 * 3^1 which is equal to 3<BR>\n" );
document.write( "when n is equal to 2, An is equal to 1 * 3^2 which is equal to 9<BR>\n" );
document.write( "when n is equal to 3, An is equal to 1 * 3^3 which is equal to 27<BR>\n" );
document.write( "when n is equal to 4, An is equal to 1 * 3^4 which is equal to 81\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( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );