document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=259658>Question 259658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are.<BR>\n" );
document.write( "please tell me the solution and method of solving this type of questions using this formula for Ap:(a-d),a, (a+d) and for GP:a/r,a,ar<BR>\n" );
document.write( "the option for the above question is :A)5,7,9 B)9,7,5 C) none of these\r<BR>\n" );
document.write( "\n" );
document.write( "the above is question of AP and GP.<BR>\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 #191104 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=191104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be your starting number, d be the difference for the arithmetic progression.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2B%28A%2Bd%29%2B%28A%2Bd%2Bd%29=21 ALIGN=MIDDLE  ALT=\"A%2B%28A%2Bd%29%2B%28A%2Bd%2Bd%29=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3A%2B3d=21 ALIGN=MIDDLE  ALT=\"3A%2B3d=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2Bd=7 ALIGN=MIDDLE  ALT=\"A%2Bd=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from the geometric progression information,<BR>\n" );
document.write( "First:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2B1 ALIGN=MIDDLE  ALT=\"A%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Second:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2Bd%2B5 ALIGN=MIDDLE  ALT=\"A%2Bd%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Third:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2Bd%2Bd%2B15=A%2B2d%2B15 ALIGN=MIDDLE  ALT=\"A%2Bd%2Bd%2B15=A%2B2d%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since they are in geometric progression, each successive pair equals the common ratio.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2Bd%2B5%29%2F%28A%2B1%29=%28A%2B2d%2B15%29%2F%28A%2Bd%2B5%29 ALIGN=MIDDLE  ALT=\"%28A%2Bd%2B5%29%2F%28A%2B1%29=%28A%2B2d%2B15%29%2F%28A%2Bd%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From eq. 1, you know,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2Bd=7 ALIGN=MIDDLE  ALT=\"A%2Bd=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2Bd%2B5%29%2F%28A%2B1%29=%28A%2B2d%2B15%29%2F%28A%2Bd%2B5%29 ALIGN=MIDDLE  ALT=\"%28A%2Bd%2B5%29%2F%28A%2B1%29=%28A%2B2d%2B15%29%2F%28A%2Bd%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2B5%29%2F%28A%2B1%29=%287%2Bd%2B15%29%2F%287%2B5%29 ALIGN=MIDDLE  ALT=\"%287%2B5%29%2F%28A%2B1%29=%287%2Bd%2B15%29%2F%287%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28A%2B1%29=%2822%2Bd%29%2F12 ALIGN=MIDDLE  ALT=\"12%2F%28A%2B1%29=%2822%2Bd%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2B1%29%2822%2Bd%29=144 ALIGN=MIDDLE  ALT=\"%28A%2B1%29%2822%2Bd%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again using eq. 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2Bd=7 ALIGN=MIDDLE  ALT=\"A%2Bd=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=7-A ALIGN=MIDDLE  ALT=\"d=7-A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2B1%29%2822%2Bd%29=144 ALIGN=MIDDLE  ALT=\"%28A%2B1%29%2822%2Bd%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2B1%29%2822%2B7-A%29=144 ALIGN=MIDDLE  ALT=\"%28A%2B1%29%2822%2B7-A%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2B1%29%2829-A%29=144 ALIGN=MIDDLE  ALT=\"%28A%2B1%29%2829-A%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29A-A%5E2%2B29-A=144 ALIGN=MIDDLE  ALT=\"29A-A%5E2%2B29-A=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A%5E2%2B28A%2B29=144 ALIGN=MIDDLE  ALT=\"-A%5E2%2B28A%2B29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A%5E2%2B28A-115=0 ALIGN=MIDDLE  ALT=\"-A%5E2%2B28A-115=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-28A%2B115=0 ALIGN=MIDDLE  ALT=\"A%5E2-28A%2B115=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can factor, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A-23%29%28A-5%29=0 ALIGN=MIDDLE  ALT=\"%28A-23%29%28A-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-23=0 ALIGN=MIDDLE  ALT=\"A-23=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=23 ALIGN=MIDDLE  ALT=\"A=23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=7-A ALIGN=MIDDLE  ALT=\"d=7-A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=7-23=-16 ALIGN=MIDDLE  ALT=\"d=7-23=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-5=0 ALIGN=MIDDLE  ALT=\"A-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=5 ALIGN=MIDDLE  ALT=\"A=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=7-A ALIGN=MIDDLE  ALT=\"d=7-A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=7-5=2 ALIGN=MIDDLE  ALT=\"d=7-5=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A) (5,7,9) is one solution. <BR>\n" );
document.write( "But (23, 7, -9) is also a solution.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );