document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516344>Question 516344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Method of Finite Differences to find a function for the following sequences. Explain your process.<BR>\n" );
document.write( "a. 9, 5, -5, -21, . . .<BR>\n" );
document.write( "b. 2.5, 6, 13.5, 25, . . .\r<BR>\n" );
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document.write( "Ok...This is what I have done.<BR>\n" );
document.write( "For \"a\" there is a second common difference of -6, and for \"b\" there is a second common difference of 4. Now I have forgotten how to use the method of finite differences. I remember learning something about generating the sequence by using:<BR>\n" );
document.write( "a_n+1 = a_n + (the second common difference)n + something?<BR>\n" );
document.write( "But I’m not sure this is what I need to use…I’m sure if I could just see “a” done I can do “b”. Thanks in advance for the help!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344346 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=344346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Use the Method of Finite Differences to find a function for the following sequences. Explain your process.<BR>\n" );
document.write( "a. 9, 5, -5, -21, . . .<BR>\n" );
document.write( "b. 2.5, 6, 13.5, 25, . . .\r<BR>\n" );
document.write( "\n" );
document.write( "Ok...This is what I have done.<BR>\n" );
document.write( "For \"a\" there is a second common difference of -6, and for \"b\" there is a second common difference of 4. Now I have forgotten how to use the method of finite differences. I remember learning something about generating the sequence by using:<BR>\n" );
document.write( "a_n+1 = a_n + (the second common difference)n + something?<BR>\n" );
document.write( "But I’m not sure this is what I need to use…I’m sure if I could just see “a” done I can do “b”. Thanks in advance for the help!\r<BR>\n" );
document.write( "\n" );
document.write( "----------------<BR>\n" );
document.write( "a. 9, 5, -5, -21, .<BR>\n" );
document.write( ";;;;;-4;;-10;-16<BR>\n" );
document.write( ";;;;;;;-6;;;-6\r<BR>\n" );
document.write( "\n" );
document.write( "----<BR>\n" );
document.write( "Form f(x) = ax^2+bx+c<BR>\n" );
document.write( "(1) = a + b + c = 9<BR>\n" );
document.write( "f(2) = 4a +2b + c = 5<BR>\n" );
document.write( "f(3) = 9a+3b + c  = -5<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Solve for a,b,c,d<BR>\n" );
document.write( "I solved the system using a Matrix Method to get:<BR>\n" );
document.write( " a = -3; b = 5; c = 7<BR>\n" );
document.write( "==================================<BR>\n" );
document.write( "Equation f(x) = -3x^2 + 5x + 7<BR>\n" );
document.write( "f(1) = 9<BR>\n" );
document.write( "f(2) = 5<BR>\n" );
document.write( "f(3) = -5<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The site below illustrates the method of Finite Differences\r<BR>\n" );
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document.write( "http://mathforum.org/library/drmath/view/53223.html </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );