document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127067>Question 1127067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5;x;y is an arithmetic sequence and x;y;81 is a geometric sequence.All terms in the sequence are integers.calculate the value of x and y. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743448 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A.S. 5, x, y<BR>\n" );
document.write( "G.S. x, y, 81<BR>\n" );
document.write( "Let d = the common difference of the A.S.<BR>\n" );
document.write( "Thus:<BR>\n" );
document.write( "x - 5 = d<BR>\n" );
document.write( "y - x = d<BR>\n" );
document.write( "y - 5 = 2d -> y - 5 = 2(x - 5) -> y = 2x - 5<BR>\n" );
document.write( "So the terms of the G.S. are:<BR>\n" );
document.write( "x, 2x - 5, 81<BR>\n" );
document.write( "The common ratio r = (2x - 5)/x = 81/(2x - 5)<BR>\n" );
document.write( "Solve for x:<BR>\n" );
document.write( "(2x - 5)/x = 81/(2x - 5)<BR>\n" );
document.write( "(2x - 5)^2 = 81x<BR>\n" );
document.write( "4x^2 - 101x + 25 = 0<BR>\n" );
document.write( "This can be factored as (4x - 1)(x - 25)<BR>\n" );
document.write( "Since the terms are all integers, x = 25<BR>\n" );
document.write( "Hence y = 2*25 - 5 = 45<BR>\n" );
document.write( "Ans: x = 25, y = 45<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );