document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190617>Question 1190617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Consider the arithmetic series 3+7+11+15+19, answer the questions below <BR>\n" );
document.write( "a (i) T1 and S1<BR>\n" );
document.write( "(ii) Express T2 in terms of S2 and S1<BR>\n" );
document.write( "(iii) T4 and S4<BR>\n" );
document.write( "(iv) Express T3 in terms of S4 and S3<BR>\n" );
document.write( "Use the pattern you observed in previous questions to express T100 in terms of S100 and S99\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822323 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52782)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "                     (a) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(i)  T1 is the first term, which is 3.\r\n" );
document.write( "\r\n" );
document.write( "     S1 is the first term, which is 3, again.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     T2 is the second term, which is 7.\r\n" );
document.write( "\r\n" );
document.write( "     S2 is the sum of the first two terms, which is 3+7 = 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(ii)        T2 = S2 - S1, which is OBVIOUS.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(iii)  T4 is the 4th term  15.\r\n" );
document.write( "\r\n" );
document.write( "       S4 is the sum of the first 4 terms  3 + 7 + 11 + 15.\r\n" );
document.write( "\r\n" );
document.write( "             (calculate it on your own, if you need)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(iV)  T3 = S3 - S2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      which means that the third term of the AP is the sum of the first 3 terms MINUS the sum of the first two terms.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      If you think one minute, you will find this formula OBVIOUS and trivial.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And the last assignment /formula is\r\n" );
document.write( "\r\n" );
document.write( "      T100 = S100 - S99.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It expresses that obvious fact that the 100th term is the sum of the first 100 terms MUNIS the sum of the first 99 terms.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Happy learning (!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For introductory lessons on arithmetic progressions see \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lessons are the part of this online textbook under the topic <U>\"Arithmetic progressions\"</U>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "into your archive and use when it is needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );