document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005464>Question 1005464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the 6th and 8th terms of an A.P is 142 . If the fourth term is 49 , (a) find the first term . (b) the common difference . (c) the sum of the first seven terms of the progression. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621718 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=621718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the 6th and 8th terms of an A.P is 142 . If the fourth term is 49 , (a) find the first term . (b) the common difference . (c) the sum of the first seven terms of the progression. <BR>\n" );
document.write( "----<BR>\n" );
document.write( "6th term:: a(1)+5d <BR>\n" );
document.write( "8th term:: a(1)+7d<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "sum = 142<BR>\n" );
document.write( "2*a(1) + 12d = 142<BR>\n" );
document.write( "----<BR>\n" );
document.write( "a(1) + 6d = 71<BR>\n" );
document.write( "=====<BR>\n" );
document.write( "4th term:: a(1) + 3d = 49<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "a(1) + 6d = 71<BR>\n" );
document.write( "a(1) + 3d = 49<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Subtract and solve for \"d\"::<BR>\n" );
document.write( "3d = 22<BR>\n" );
document.write( "d = 22/3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve for a(1)::<BR>\n" );
document.write( "a(1) + 3d = 49<BR>\n" );
document.write( "a(1) + 22 = 49<BR>\n" );
document.write( "a(1) = 27<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Sum the 1st 7 terms:<BR>\n" );
document.write( "S(7) = (7/2)(a(1)+a(7)]<BR>\n" );
document.write( "S(7) = (7/2)(27+71)<BR>\n" );
document.write( "S(7) = (7/2)(98)<BR>\n" );
document.write( "S(7) = 7*49 = 343<BR>\n" );
document.write( "---------------\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );