document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166128>Question 1166128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Take a look at the sequence of square numbers listed in the first row of numbers<BR>\n" );
document.write( "below. The first several terms of the sequence are listed and, below that, the first<BR>\n" );
document.write( "differences of the two numbers immediately above, and below that are the<BR>\n" );
document.write( "differences of the differences (i.e., the second differences).<BR>\n" );
document.write( "1 4 9 16 25<BR>\n" );
document.write( "3 5 7<BR>\n" );
document.write( "2 2<BR>\n" );
document.write( "9<BR>\n" );
document.write( "2<BR>\n" );
document.write( "2<BR>\n" );
document.write( "36<BR>\n" );
document.write( "11<BR>\n" );
document.write( "2<BR>\n" );
document.write( "13<BR>\n" );
document.write( "2<BR>\n" );
document.write( "Notice that for the sequence n2 the second differences are all 2.<BR>\n" );
document.write( "2. Make a conjecture as to what will happen with the fourth powers and the fifth<BR>\n" );
document.write( "powers. Make a conjecture about the differences and the resulting constant for<BR>\n" );
document.write( "the sequence of kth powers of nk where k is a positive integer. [This Exploration<BR>\n" );
document.write( "can be done by hand, or with a calculator, or in a spreadsheet program such as<BR>\n" );
document.write( "Excel.]<BR>\n" );
document.write( "3. If you are given a sequence of kth powers ank, is there a way to figure out the<BR>\n" );
document.write( "value of the coefficient a?<BR>\n" );
document.write( "I only need assistance with number 2 I included number 2 to help number 3 make better sense.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790612 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</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=790612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "For n = 3, you can make your own experiment and to formulate your own conjecture then.\r<BR>\n" );
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document.write( "Try the third difference, in this case.\r<BR>\n" );
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