document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137191>Question 1137191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the recursive formula for 5,15,30,50,...<BR>\n" );
document.write( "please show work on how it's done </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755028 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the method of level of common difference <BR>\n" );
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document.write( "5, 15, 30, 50<BR>\n" );
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document.write( "Level 1<BR>\n" );
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document.write( "10, 15, 20<BR>\n" );
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document.write( "Level 2<BR>\n" );
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document.write( "5, 5<BR>\n" );
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document.write( "Level 2 has a common difference which tells us that we have an n^2 term<BR>\n" );
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document.write( "We can write the following equations for the known terms<BR>\n" );
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document.write( "1) a(1)^2 +b(1) +c = a +b +c = 5<BR>\n" );
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document.write( "2) a(2)^2 +b(2) +c = 4a +2b +c = 15<BR>\n" );
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document.write( "3) a(3)^2 +b(3) +c = 9a +3b +c = 30<BR>\n" );
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document.write( "4) a(4)^2 +b(4) +c = 16a +4b +c = 50<BR>\n" );
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document.write( "Since we have 3 unknowns(a, b, c), we can use three equations to form an augmented matrix<BR>\n" );
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document.write( "1 1 1 5<BR>\n" );
document.write( "4 2 1 15<BR>\n" );
document.write( "9 3 1 30<BR>\n" );
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document.write( "Use your favorite method to solve augmented matrices <BR>\n" );
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document.write( "a = 2.5, b = 2.5, c = 0<BR>\n" );
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document.write( "the formula for the nth term is<BR>\n" );
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document.write( "x(n) = 2.5n^2 +2.5n<BR>\n" );
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document.write( "x(1) is the first term of the sequence, then<BR>\n" );
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document.write( "5) x(n) = x(n-1) +2a(n) +d<BR>\n" );
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document.write( "x(1)=5, 2a = 2(2.5) = 5, use equation 5 to find d<BR>\n" );
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document.write( "x(2) = 5 +5(2) +d = 15<BR>\n" );
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document.write( "d = 0<BR>\n" );
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document.write( "Therefore, the recursive function is<BR>\n" );
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document.write( "x(1) = 5,<BR>\n" );
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document.write( "x(n) = x(n-1) +5n<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );