document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772418>Question 772418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 41, 31, 23, 17, 11,______<BR>\n" );
document.write( "what would be the next term?\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Urvashi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470853 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let the first term be term 0, the second be term 1, and so on.\r<BR>\n" );
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document.write( "Then create a set of ordered pairs, (0,41), (1,31), (2, 23), and so on.\r<BR>\n" );
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document.write( "Now that you have a set of five ordered pairs, you can find a fourth degree polynomial function that exactly fits the data.\r<BR>\n" );
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document.write( "The general 4th degree polynomial function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ ax^4\ +\ bx^3\ +\ cx^2\ +\ dx\ +\ e\">\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(0)\ =\ 41\">, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(0)\ =\ a(0)^4\ +\ b(0)^3\ +\ c(0)^2\ +\ d(0)\ +\ e\ =\ 41\">\r<BR>\n" );
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document.write( "From which it is obvious that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e\ =\ 41\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(1)\ =\ a(1)^4\ +\ b(1)^3\ +\ c(1)^2\ +\ d(1)\ +\ 41\ =\ 31\">\r<BR>\n" );
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document.write( "From which we derive:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\ +\ b\ +\ c\ +\ d\ =\ -10\">\r<BR>\n" );
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document.write( "Similarly, you can derive three other linear equations in a, b, c, and d.  I'll leave this as an exercise for the student.\r<BR>\n" );
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document.write( "You should now have the following 4 equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\ +\ b\ +\ c\ +\ d\ =\ -10\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 16a\ +\ 8b\ +\ 4c\ +\ 2d\ =\ -18\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 81a\ +\ 27b\ +\ 9c\ +\ 3d\ =\ -24\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 256a\ +\ 64b\ +\ 16c\ +\ 4d\ =\ -30\">\r<BR>\n" );
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document.write( "Solve the 4X4 system by any convenient means (I use the MDTERM function in Excel and Cramer's rule)\r<BR>\n" );
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document.write( "Once you have the four coefficients a, b, c, and d, write your function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ ax^4\ +\ bx^3\ +\ cx^2\ +\ dx\ +\ 41\">\r<BR>\n" );
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document.write( "By plugging in the values.\r<BR>\n" );
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document.write( "Finally, calcualate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(5)\">.  Write back and let me know what you got.  I'll let you know if you did it correctly.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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