document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265723>Question 265723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> arithmetic sequence a10=x+3 a11=2x+7 a12=4x-2 which term equals 186 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195445 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=195445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know the following:<BR>\n" );
document.write( "a10 = x+ 3<BR>\n" );
document.write( "a11 = 2x+7<BR>\n" );
document.write( "a12 = 4x-2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since this is arithmetic all differences are \"common\" or the same<BR>\n" );
document.write( "a11 - a10: x+4<BR>\n" );
document.write( "a12 - a11: 2x - 9<BR>\n" );
document.write( "set these equal and solve for x to get<BR>\n" );
document.write( "x+ 4 = 2x - 9<BR>\n" );
document.write( "subtract x to get<BR>\n" );
document.write( "4 = x - 9<BR>\n" );
document.write( "add 9  to get<BR>\n" );
document.write( "x = 13<BR>\n" );
document.write( "now we see that <BR>\n" );
document.write( "a10 = 13 + 3 =16<BR>\n" );
document.write( "a11 = 2*13 + 7 = 33<BR>\n" );
document.write( "a12 = 4*13 - 2 = 50<BR>\n" );
document.write( "the common difference is 17 and the tn formula is<BR>\n" );
document.write( "Tn = 17n - 154<BR>\n" );
document.write( "Now we want the nth term at 186 so we get<BR>\n" );
document.write( "186 = 17n - 154<BR>\n" );
document.write( "add 154 to get<BR>\n" );
document.write( "17n = 340<BR>\n" );
document.write( "n = 20 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );