document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134390>Question 1134390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of 8th terms of an AP is 160 while the sum of 20 terms is 880. Find (a) the 43rd term (b) the sum of 12 terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751762 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let a and d be the first term and common difference, respectively.  Then<br><BR>\n" );
document.write( "the 8th term is a+7d<BR>\n" );
document.write( "the 20th term is a+19d<br><BR>\n" );
document.write( "The sum of the first 8 terms is<BR>\n" );
document.write( "(a)+(a+d)+(a+2d)+...+(a+7d) = 8a+28d<br><BR>\n" );
document.write( "The sum of the first 20 terms is<BR>\n" );
document.write( "(a)+(a+d)+(a+2d)+...+(a+19d) = 20a+190d<br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%2B28d+=+160 ALIGN=MIDDLE  ALT=\"8a%2B28d+=+160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20a%2B190d+=+880 ALIGN=MIDDLE  ALT=\"20a%2B190d+=+880\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40a%2B140d+=+800 ALIGN=MIDDLE  ALT=\"40a%2B140d+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40a%2B380d+=+1760 ALIGN=MIDDLE  ALT=\"40a%2B380d+=+1760\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240d+=+960 ALIGN=MIDDLE  ALT=\"240d+=+960\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+4 ALIGN=MIDDLE  ALT=\"d+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%2B112+=+160 ALIGN=MIDDLE  ALT=\"8a%2B112+=+160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a+=+48 ALIGN=MIDDLE  ALT=\"8a+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+6 ALIGN=MIDDLE  ALT=\"a+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The first term is 6 and the common difference is 4.<br><BR>\n" );
document.write( "The 43rd term is a+42d = 6+42(4) = 6+168 = 174<br><BR>\n" );
document.write( "The sum of the first 12 terms is<BR>\n" );
document.write( "(a)+(a+d)+(a+2d)+...+(a+11d) = 12a+66d = 12(6)+66(4) = 72+264 = 336<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );