document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193591>Question 1193591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of this series that is not arithmetic or geometric,<BR>\n" );
document.write( "1+2+4+5+7+8....+95+97+98\r<BR>\n" );
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document.write( "can someone help, a few of us have been trying to figure this out, our teacher said its solvable but I don't even know where to start, thankyou </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825650 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=825650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have received two responses that show two very different ways of solving the problem, both of which are valid.<br><BR>\n" );
document.write( "Here is a third (still very different) method....<br><BR>\n" );
document.write( "The sequence is clearly neither geometric nor arithmetic.  But we can make it into an arithmetic sequence by pairing the terms:<br><BR>\n" );
document.write( "1+2=3<BR>\n" );
document.write( "4+5=9<BR>\n" );
document.write( "7+8=15<BR>\n" );
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document.write( "97+98=195<br><BR>\n" );
document.write( "So the sum is<br><BR>\n" );
document.write( "3+9+15+...+195<br><BR>\n" );
document.write( "That is an arithmetic sequence with first term 3, last term 195, and common difference 6.  The sum of the sequence is<br><BR>\n" );
document.write( "(number of terms) times (average of all the terms)<br><BR>\n" );
document.write( "Since the sequence is arithmetic, the average of all the terms is the average of the first and last: (3+195)/2=99<br><BR>\n" );
document.write( "The number of terms is<br><BR>\n" );
document.write( "(last term minus first term), divided by 6, plus 1<br><BR>\n" );
document.write( "The difference between the first and last terms, divided by the common difference, tells you the number of terms AFTER THE FIRST ONE; that's why you need to add 1 at the end.<br><BR>\n" );
document.write( "195-3=192; 192/6=32; 32+1=33<br><BR>\n" );
document.write( "So we have a sequence of 33 terms with an average of 99; the sum is<br><BR>\n" );
document.write( "33(99)=33(100-1) = 3300-33 = 3267<br><BR>\n" );
document.write( "ANSWER: 3267<br><BR>\n" );
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