document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046328>Question 1046328</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Take a look at the following sums:\r<BR>\n" );
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document.write( "1=1<BR>\n" );
document.write( "1+3=4<BR>\n" );
document.write( "1+3+5=9<BR>\n" );
document.write( "1+3+5+7=16<BR>\n" );
document.write( "1+3+5+7+9=25\r<BR>\n" );
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document.write( "a.  Come up with a conjecture about the sum when you add the first n odd numbers.  For example when you added the first five odd numbers ( 1+3+5+7+9) what do you get?  What if I wanted to add the first 10 odd numbers? Or 100? \r<BR>\n" );
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document.write( "b.  Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have four squares and you add on five more, what can you make? \r<BR>\n" );
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document.write( "c.  Is there a similar pattern for adding the first n even numbers? \r<BR>\n" );
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document.write( "2=2<BR>\n" );
document.write( "2+4=6<BR>\n" );
document.write( "2+4+6=12<BR>\n" );
document.write( "2+4+6+8= 20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661817 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=661817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1=1<BR>\n" );
document.write( "1+3=4<BR>\n" );
document.write( "1+3+5=9<BR>\n" );
document.write( "1+3+5+7=16<BR>\n" );
document.write( "1+3+5+7+9=25<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "Regarding the sum of first \"n\" odd/even natural numbers, see the lessons \r<BR>\n" );
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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" );
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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" );
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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" );
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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" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Chocolate-bars-and-arithmetic-progressions.lesson>Chocolate bars and arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-and-arithmetic-progressions.lesson>Mathematical induction and arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-arithmetic-progressions.lesson>One characteristic property of arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-arithmetic-progressions.lesson>Solved problems on arithmetic progressions</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );