document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936170>Question 936170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "How can i find the first and sum of the first 14 terms of an arithmetic sequence if i only know that the sum of the 3rd and 7th term is 24 and difference between the 6th and 4th is 4?\r<BR>\n" );
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document.write( "Thanks alot :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569609 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula for n th term ( tn) = a+(n-1)d<BR>\n" );
document.write( "where a= first term<BR>\n" );
document.write( "      d= common difference<BR>\n" );
document.write( "      n = no of terms<BR>\n" );
document.write( "so 3rd term  (t3)= a+(3-1)d<BR>\n" );
document.write( "                  = a+2d<BR>\n" );
document.write( "similarly<BR>\n" );
document.write( "          7 the term   t(7)  = a+(7-1)d<BR>\n" );
document.write( "                               =a+6d\r<BR>\n" );
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document.write( "6 th term  (t6)=  a+5d<BR>\n" );
document.write( "  4 th term (t4) = a+3d<BR>\n" );
document.write( "  sum of the 3rd and 7th term is 24<BR>\n" );
document.write( "so <BR>\n" );
document.write( "            (a+2d) +(a+6d) = 24<BR>\n" );
document.write( "                 2a+8d  =24...................eq(1)\r<BR>\n" );
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document.write( "difference between the 6th and 4th is 4<BR>\n" );
document.write( " (a+5d)-(a+3d) = 4<BR>\n" );
document.write( "     2d  = 4<BR>\n" );
document.write( " divide with 2 on both sides<BR>\n" );
document.write( "  2d/d  = 4/4<BR>\n" );
document.write( " d= 2<BR>\n" );
document.write( "put d=2 in eq(1) <BR>\n" );
document.write( "         2a+8*2=24<BR>\n" );
document.write( "            2a+16=24<BR>\n" );
document.write( "          2a  =24-16<BR>\n" );
document.write( "   2a= 8<BR>\n" );
document.write( "   divide with 2 on both sides<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a%2F2++=+8%2F2 ALIGN=MIDDLE  ALT=\"+2a%2F2++=+8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "          a= 4<BR>\n" );
document.write( "so , first term   (a) = 4<BR>\n" );
document.write( "sum of n terms in Arithmetic series  =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28n%2F2%29%282a%2B%28n-1%29d%29 ALIGN=MIDDLE  ALT=\"+%28n%2F2%29%282a%2B%28n-1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " sum of first 14 terms  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2814%2F2%29%282%2A4+%2B%2814-1%292%29 ALIGN=MIDDLE  ALT=\"+%2814%2F2%29%282%2A4+%2B%2814-1%292%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "             =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%288%2B13%2A2%29 ALIGN=MIDDLE  ALT=\"7%288%2B13%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "           =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%288%2B26%29 ALIGN=MIDDLE  ALT=\"7%288%2B26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2834%29 ALIGN=MIDDLE  ALT=\"7%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "       =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=238 ALIGN=MIDDLE  ALT=\"238\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Result : first term  = 4 , sum  = 238\r<BR>\n" );
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document.write( " </SPAN>\n" );
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