document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939630>Question 939630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572605 by </B><A HREF=/tutors/aboutme.mpl?userid=laoman><B>laoman(51)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=laoman><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=laoman><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For an aritmetic sequence, tn= a+(n-1)*d<BR>\n" );
document.write( "Where a is the first term, n is the no. of terms and d is the common difference,<BR>\n" );
document.write( "Given t23 = a+22d=519 and t71 = a+70d=1503<BR>\n" );
document.write( "To find t114 = a+113d<BR>\n" );
document.write( "Let's find the values of a and d using the simultaneous equations above<BR>\n" );
document.write( "We have,<BR>\n" );
document.write( "a+22d=519<BR>\n" );
document.write( "a+70d=1503<BR>\n" );
document.write( "Subtracting the second equation from the first,<BR>\n" );
document.write( "a-a+22d-70d=519-1503<BR>\n" );
document.write( "-48d = -984<BR>\n" );
document.write( "d = -984/-48 = 20.5<BR>\n" );
document.write( "d =20.5<BR>\n" );
document.write( "From the first eqn, a +22d = 519<BR>\n" );
document.write( "a=519-22*d=519-22*20.5=519-451<BR>\n" );
document.write( "a=68\r<BR>\n" );
document.write( "\n" );
document.write( "Now we know a=68 and d=20.5<BR>\n" );
document.write( "t114 = a+113d =68+113*20.5 = 68+2316.5<BR>\n" );
document.write( "t114=2384.5\r<BR>\n" );
document.write( "\n" );
document.write( "QED </SPAN>\n" );
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