document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254675>Question 254675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three numbers form an arithmetic sequence, common difference being 11. If first number is decreased by 6, second number decreased by 1, and third number doubled, resulting numbers form a geometric sequence. determine the numbers that form the arithmetic sequence\r<BR>\n" );
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document.write( "Answer is -26, -15, -4, 14, 25, 36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187022 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the first term be A<BR>\n" );
document.write( "Let the second term be A + 11<BR>\n" );
document.write( "Let the third term be A + 22<BR>\n" );
document.write( "we know that common difference, d, is 11.<BR>\n" );
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document.write( "A - 6, A + 10, 2(A+22)<BR>\n" );
document.write( "is now a geometric sequence. They have common ratios which can be expressed as<BR>\n" );
document.write( "(A+10)/(A-6) = (2A+44)/(A+10)<BR>\n" );
document.write( "Cross multiplying, we get<BR>\n" );
document.write( "(A+10)^2 = (2A+44)(A-6)<BR>\n" );
document.write( "A^2 + 20A + 100 = 2A^2 + 32A -264<BR>\n" );
document.write( "set = 0 as<BR>\n" );
document.write( "A^2 + 12A -364 = 0<BR>\n" );
document.write( "(A - 14)(a + 26) = 0<BR>\n" );
document.write( "A = 14 or A = -26<BR>\n" );
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document.write( "If A = 14, then the arithmetic sequence is<BR>\n" );
document.write( "14, 25, 36<BR>\n" );
document.write( "and the geometric sequence is<BR>\n" );
document.write( "8, 24, 72 <BR>\n" );
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document.write( "If A = -26, then the arithmetic sequence is<BR>\n" );
document.write( "-26, -15, -4<BR>\n" );
document.write( "and the geometric sequence is<BR>\n" );
document.write( "-32, -16, -8 </SPAN>\n" );
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