document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172506>Question 1172506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the 7th term of an ap is 17 and the13th term is 12 more than the 7th term find the sum of the first 18th terms of the ap </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797589 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=797589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are dozens of similar ways to solve a problem like this.  Here is what I would do....<br><BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "Arithmetic sequence<BR>\n" );
document.write( "7th term 17<BR>\n" );
document.write( "13th term 12 more than the 7th term<br><BR>\n" );
document.write( "To find:<BR>\n" );
document.write( "Sum of first 18 terms<br><BR>\n" );
document.write( "Solution....<br><BR>\n" );
document.write( "(1) The sum of the first 18 terms of an arithmetic sequence is 18 times the average of all the terms, which in a sequence with 18 terms is 18 times the average of the 9th and 10th terms (the two terms \"in the middle\").<br><BR>\n" );
document.write( "(2) The 13th term is the 7th term plus 13-7=6 times the common difference; since the 13th term is 12 more than the 7th, the common difference is 12/6 = 2.<br><BR>\n" );
document.write( "(3) So the 7th, 8th, 9th, and 10th terms of the sequence are 17, 19, 21, and 23.<br><BR>\n" );
document.write( "ANSWER: The sum of the first 18 terms is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%28%2821%2B23%29%2F2%29+=+18%2822%29+=+%2820-2%29%2820%2B2%29+=+20%5E2-2%5E2+=+400-4+=+396 ALIGN=MIDDLE  ALT=\"18%28%2821%2B23%29%2F2%29+=+18%2822%29+=+%2820-2%29%2820%2B2%29+=+20%5E2-2%5E2+=+400-4+=+396\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );