document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064171>Question 1064171</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term of the geometric progression? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679231 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=679231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term of the geometric progression? <BR>\n" );
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document.write( "arithmetic progression:: a; a+d; a+2d<BR>\n" );
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document.write( "a = 9<BR>\n" );
document.write( "a+d + 2 = d+11<BR>\n" );
document.write( "a+2d + 20 = 2d+ 29<BR>\n" );
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document.write( "geometric progression:: a; ar; ar^2<BR>\n" );
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document.write( "a = 9<BR>\n" );
document.write( "ar = d+11<BR>\n" );
document.write( "ar^2 = 2d+29<BR>\n" );
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document.write( "r = ar/a = (d+11)/9<BR>\n" );
document.write( "r = ar^2/ar = (2d+29)/(d+11)<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "r = r<BR>\n" );
document.write( "(d+11)/9 = (2d+29)/(d+11)<BR>\n" );
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document.write( "18d + 261 = d^2 + 22d + 121<BR>\n" );
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document.write( "d^2 + 4d -40 = 0<BR>\n" );
document.write( "d = 4.63<BR>\n" );
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document.write( "Ans: 2d+29 = 2*4.63+29 = 38.26<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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