document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196447>Question 196447</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618608532/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> In exercises 1-6, construct a difference table to predict the next term of each sequence. \r<BR>\n" );
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document.write( "4.) 0, 10, 24, 56, 112, 190 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147255 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=147255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x,,,,,,1,,,,,2,,,,3,,,,,,4,,,,,5,,,,,,6<BR>\n" );
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document.write( "f(x),,,,0,,,10,,,24...56,,,112,,,190,,,,,,,,base<BR>\n" );
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document.write( "d,,,,,,,,,,10,,,,14,,,32,,,56,,,78,,,,,,,,,,,,,1st degree<BR>\n" );
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document.write( "d,,,,,,,,,,,,,,,,,4,,,,,18,,,24,,,22,,,,,,,,,,,,,,2nd  degree<BR>\n" );
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document.write( "d,,,,,,,,,,,,,,,,,,,,,14,,,,6,,,,,-2,,,,,,,,,,,,,,,,,3rd  degree<BR>\n" );
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document.write( "d,,,,,,,,,,,,,,,,,,,,,,,,,,-8,,,,-8,,,,,,,,,,,,,,,,,,,4th  degree<BR>\n" );
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document.write( "This  defines  f(x)  =  ax^4  +bx^3 + cx^2 + dx +e<BR>\n" );
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document.write( "(1)  0 = a(1)^4  +b(1)^3 +c(1)^2 +d(1)^1 +e<BR>\n" );
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document.write( "(2) 10 = a(2)^4 +b(2)^3 +c(2)^2 +d(2)^1 +e<BR>\n" );
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document.write( "(3) 24 = a(3)^4  +b(3)^3 +c(3)^2 +d(3)^1 +e<BR>\n" );
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document.write( "(4) 56 = a(4)^4 +b(4)^3 +c(4)^2 +d(4)^1 +e<BR>\n" );
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document.write( "(5) 112  =a(5)^4 +b(5)^3  +c(5)^2 +d(5)^1 +e<BR>\n" );
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document.write( "(6) 190 = a(6)^4 +b(6)^3 +c(6)^2 +d(6)^1 +e<BR>\n" );
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document.write( "now  solving  these  simultaneously,  using successive  substitutions (and  mult),  <BR>\n" );
document.write( "or  matrix  computation<BR>\n" );
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document.write( "Results  in approx,,, f(x) = -.03 x^4 +1.49x^3 -7.32x^2 +21.93x-16.07<BR>\n" );
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document.write( "checking  shows  good  agreement  at  low  end,   but  about  70 %  of  actual  at  high  end<BR>\n" );
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document.write( "making  this  correction,,,f(7) = 311  approx<BR>\n" );
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document.write( "Time  does  not  permit any  further  computation, but  perhaps  this  will  give  you  a  good  start </SPAN>\n" );
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