document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918754>Question 918754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please explain what recursive and explicit formulas in algebra are. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557238 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=557238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a recursive formula works off the previous number in the sequence.\r<BR>\n" );
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document.write( "an explicit formula derives a number in the sequence based on a formula  that doesn't depend on knowing the previous number.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "An = An-1 + 4 is a recursive formula.<BR>\n" );
document.write( "you would start with a known number, like A1 = 5<BR>\n" );
document.write( "then each succeeding number would depend on the value of the preceding number.\r<BR>\n" );
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document.write( "A2 = A1 + 4<BR>\n" );
document.write( "A3 = A2 + 4<BR>\n" );
document.write( "A4 = A3 + 4\r<BR>\n" );
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document.write( "if A1 = 5, then A2 = 9 and A3 = 13 and A4 = 17, etc.\r<BR>\n" );
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document.write( "If you wanted to know the value of A10, you would need to know the value of A9.\r<BR>\n" );
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document.write( "You might be able to figure out what A10 would be directly, but it wouldn't be easy and would require you to do some thinking or creating a new formula to figure it out.\r<BR>\n" );
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document.write( "An explicit formula allows you to find the number in a sequence without having to know the previous number.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "An = A1 + (n-1)d\r<BR>\n" );
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document.write( "Once you know A1 and d, you can figure out the value of A10 directly.\r<BR>\n" );
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document.write( "If A1 = 5 and d = 4, A4 would be equal to 5 + 3*4 = 5 + 12 = 17\r<BR>\n" );
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document.write( "A10 would be equal to 5 + 9*4 = 5 + 36 = 41.\r<BR>\n" );
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document.write( "The whole sequence up to A10 is:\r<BR>\n" );
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document.write( "5<BR>\n" );
document.write( "9<BR>\n" );
document.write( "13<BR>\n" );
document.write( "17<BR>\n" );
document.write( "21<BR>\n" );
document.write( "25<BR>\n" );
document.write( "29<BR>\n" );
document.write( "33<BR>\n" );
document.write( "37<BR>\n" );
document.write( "41\r<BR>\n" );
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document.write( "in algebra, these formulas are usually defined in reference to sequences.\r<BR>\n" );
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document.write( "here's a tutorial and some exercises that talks about recursive and explicit formulas when referencing sequences.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebralab.org/lessons/lesson.aspx?file=algebra_arithseq.xml\" target = \"_blank\">http://www.algebralab.org/lessons/lesson.aspx?file=algebra_arithseq.xml</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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