document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042037>Question 1042037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find sum of 9 terms in a<BR>\n" );
document.write( "arithmetic sequence is 207 sum of first 20 terms<BR>\n" );
document.write( "is 900 . Find fifth and twenty fifth term Find<BR>\n" );
document.write( "the sum of 100 terms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656941 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=656941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the sum of 9 terms in an arithmetic sequence is 207 and the sum of first 20 terms is 900 , <BR>\n" );
document.write( "Find fifth and twenty-fifth term <BR>\n" );
document.write( "--------<BR>\n" );
document.write( "S(9) = (a(1)+(a(1)+8d)*(9/2) = 207<BR>\n" );
document.write( "S(20) = (a(1)+(a(1)+19d)*(20/2) = 900<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "2(a(1)) + 8d = (2/9)207 = 2*23 = 46<BR>\n" );
document.write( "2(a(1)) + 19d = 90<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Subtract and solve for \"d\"::<BR>\n" );
document.write( "11d = 44<BR>\n" );
document.write( "d = 4<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Then, solve for a(1)::<BR>\n" );
document.write( "2*a(1) + 8d = 46<BR>\n" );
document.write( "2*a(1) + 32 = 46<BR>\n" );
document.write( "a(1) = 7<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Ans: a(5) = 7 + 4d = 7 + 16 = 23<BR>\n" );
document.write( "a(25) = 7 + 24d = 7 + 96 = 103<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Find the sum of 100 terms.<BR>\n" );
document.write( "s(100) = (7 + a(100))*(50) <BR>\n" );
document.write( "a(100) = 7 + 99*4 = 403<BR>\n" );
document.write( "S(100) = 410*50 = 20500<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "---------------    </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );