document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149625>Question 149625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could I please get help with the following problem:\r<BR>\n" );
document.write( "\n" );
document.write( "Find a general formula for the arithmetic sequence whose 8th term is -20 and the 17th term is -47\r<BR>\n" );
document.write( "\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109798 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it is an \"arithmetic sequence\" there is a \"constant difference\" between each number in the series.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The formula for any number within that sequence is:<BR>\n" );
document.write( "An = A1 + (n-1)d<BR>\n" );
document.write( "where<BR>\n" );
document.write( "An = value of the nth number within the series<BR>\n" );
document.write( "A1 = first value of the sequence<BR>\n" );
document.write( "n = nth term<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In your problem they don't give you the difference (d) and you are asked to find that given all the other information.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Find a general formula for the arithmetic sequence whose 8th term is -20 and the 17th term is -47.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The distance is:<BR>\n" );
document.write( "d = (-47-(-20))/(17-8)<BR>\n" );
document.write( "d = (-47+20)/(17-8)<BR>\n" );
document.write( "d = (-27)/(9)<BR>\n" );
document.write( "d = -3<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now, plug in what we know into:<BR>\n" );
document.write( "An = A1 + (n-1)d<BR>\n" );
document.write( "An = -20 + (n-1)(-3)<BR>\n" );
document.write( "An = -20 + (-3n+3)<BR>\n" );
document.write( "An = -17 - 3n  (this is what you're looking for)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For example, to find the 3rd number:<BR>\n" );
document.write( "A(3) = -17 - 3(3)<BR>\n" );
document.write( "A(3) = -17 - 9<BR>\n" );
document.write( "A(3) = -26\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );