document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258336>Question 258336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an arithmetic sequence of positive numbers, the common difference is twice the first term, and the sum of the first six terms is equal to the square of the first term. Find the first term of the sequence.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190170 by </B><A HREF=/tutors/aboutme.mpl?userid=palanisamy><B>palanisamy(496)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=palanisamy><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=190170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the first term of an arithmetic sequence be a.<BR>\n" );
document.write( "Given,the common difference is twice the first term.<BR>\n" );
document.write( "So the common difference d = 2a<BR>\n" );
document.write( "Also, the sum of the first six terms is equal to the square of the first term. <BR>\n" );
document.write( "     (6/2)(a+a+5d) = a^2<BR>\n" );
document.write( "      3(2a+5*2a) = a^2<BR>\n" );
document.write( "      3(12a)=a^2<BR>\n" );
document.write( "      36a-a^2=0<BR>\n" );
document.write( "      a(36-a) = 0<BR>\n" );
document.write( "      a=0  or  a=36<BR>\n" );
document.write( "Therefore the first term is 36        </SPAN>\n" );
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