document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472701>Question 472701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of three numbers in arithmetic sequence is  24 . If the first number is decreased by 1 , and the second is decreased by  2 , the three numbers will now be in geometric sequence.  Use algebra to SOLVE for the three numbers (no guessing and testing). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324026 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a-k, a, a+k be the three numbers which sum up to 24. It should appear evident that a = 8.\r<BR>\n" );
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document.write( "So our numbers are 8-k, 8, and 8+k. We want 7-k, 6, 8+k to be in a geometric progression. We know that the ratio between successive terms is constant, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{6}{7-k} = \frac{8+k}{6}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 36 = (7-k)(8+k) = -k^2 -k + 56\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE k^2 + k - 20 = 0\">\r<BR>\n" );
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document.write( "k = 4 or k = -5. Hence the sequences are 4,8,12 and 13,8,3 (both work). </SPAN>\n" );
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