document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57943>Question 57943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello - I am working on math superstars for fifth graders.  The problem follows:\r<BR>\n" );
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document.write( "students arrived for school in groups.  Bill was the first to arrive - consider him the first group.  Each group that arrived after Bill had two more people than  the group that arrived before it.  How many people were in school after 20 groups arrived?\r<BR>\n" );
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document.write( "I worked this out by hand, and got the number 400, however, my parents say there is a formula I can use to make this much easier.  They cannot remember it, though.  \r<BR>\n" );
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document.write( "Any help that you can provide me is appreciated.\r<BR>\n" );
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document.write( "Thank you and have a good day.\r<BR>\n" );
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document.write( "Cassidy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #39624 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=39624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Bill was the first to arrive - consider him the first group. Each group that arrived after Bill had two more people than the group that arrived before it. How many people were in school after 20 groups arrived? <BR>\n" );
document.write( "#=1+3+5+7+...+(1+19(2))<BR>\n" );
document.write( "This is an aritmetic sequence with 1st number being 1<BR>\n" );
document.write( "and the difference between consecutive terms being 2<BR>\n" );
document.write( "If you add 20 of these terms you get<BR>\n" );
document.write( "Sum = 1+3+5+7+....+35+37+39<BR>\n" );
document.write( "Now, if you write this backward you get<BR>\n" );
document.write( "Sum= 39+37+35+33..+5+3+1<BR>\n" );
document.write( "If you add these two lines term by term you will get:<BR>\n" );
document.write( "2Sum= 40+40+40+.....+40+40+40  <BR>\n" );
document.write( "And you will get this 20 times.<BR>\n" );
document.write( "So twice the Sum = 20(40)<BR>\n" );
document.write( "Sum = (1/2)*20*40=400<BR>\n" );
document.write( "The general formula is Sum(n terms)=(1/2)*n(1st term + last term)<BR>\n" );
document.write( "and is usually written S(n)=(n/2)(a+last)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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