document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=732799>Question 732799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first 100 terms of an arithmetic progression is 10000; the first, second and fifth terms of this progression are three consecutive terms of a geometric progression.  Find the first term, a, and the non-zero common difference, d. of the arithmetic progression  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448074 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=448074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> S 100 = 100/2[2a+99d]\r<BR>\n" );
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document.write( "S100 =50[2a+99d]\r<BR>\n" );
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document.write( "a, a+d, a+4d \r<BR>\n" );
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document.write( "(a+d)^2=a(a+4d)\r<BR>\n" );
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document.write( "a^2+2ad+d^2=a^2+4ad<BR>\n" );
document.write( "d^2=2ad<BR>\n" );
document.write( "d=2a\r<BR>\n" );
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document.write( "S100 =50[2a+99d]<BR>\n" );
document.write( "S100= 50*100d\r<BR>\n" );
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document.write( "S100=5000d<BR>\n" );
document.write( "10,000=5000d<BR>\n" );
document.write( "d=2<BR>\n" );
document.write( "Therefore a=1\r<BR>\n" );
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document.write( "Check\r<BR>\n" );
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document.write( "s100 = 100/2[2+198]<BR>\n" );
document.write( "s100= 50*200<BR>\n" );
document.write( "s100 = 10,000\r<BR>\n" );
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document.write( " </SPAN>\n" );
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