document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184340>Question 1184340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the indicated partial sum for the given sequence. Show the solution\r<BR>\n" );
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document.write( "4,7,10,13,...,S10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814931 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Technically, the statement of the problem needs to specify that this is an arithmetic sequence.  Simply showing the sequence as<BR>\n" );
document.write( "4,7,10,13,...<BR>\n" );
document.write( "leaves open the possibility that the following numbers could be ANY numbers.<br><BR>\n" );
document.write( "Assuming then that this is an arithmetic sequence....<br><BR>\n" );
document.write( "S10 is the sum of the first 10 terms of the sequence.<br><BR>\n" );
document.write( "The sum of ANY set of numbers is the average of the numbers, multiplied by how many there are.<br><BR>\n" );
document.write( "We are given the number of terms in this sequence; and, because the sequence is arithmetic, the average of all the terms is the average of the first and last.<br><BR>\n" );
document.write( "In an arithmetic sequence, the n-th term is the first term, plus (n-1) times the common difference.<br><BR>\n" );
document.write( "Armed with those ideas....<br><BR>\n" );
document.write( "The common difference is 3; the first term is 4; so the 10th term is 4+9(3)=31.<BR>\n" );
document.write( "The average of the terms is the average of the first and last: (4+31)/2=35/2.<BR>\n" );
document.write( "The sum of the first 10 terms is 10(35/2)=5*35=175.<br><BR>\n" );
document.write( "ANSWER: S10 = 175<br><BR>\n" );
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