document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085106>Question 1085106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need help finding the explicit formula for this problem. I'm fairly certain that I got the recursive one right, but I cannot figure out how to write the explicit formula. Any help would be much appreciated. \r<BR>\n" );
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document.write( "Thanks in advance for your help!\r<BR>\n" );
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document.write( "1. Find both a recursive rule and an explicit rule that will generate the values in the table below, provided that a0 = 3/2.   \r<BR>\n" );
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document.write( "n:     1----	2---- 3----	4----	5----	6<BR>\n" );
document.write( "an:	2---- 3----	5----	9----17----33\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699141 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5B1%5D+=+2a%5B0%5D+-+1+ ALIGN=MIDDLE  ALT=\"+a%5B1%5D+=+2a%5B0%5D+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5B2%5D+=+2a%5B1%5D+-+1+ ALIGN=MIDDLE  ALT=\"+a%5B2%5D+=+2a%5B1%5D+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "…<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5Bn%5D+=+2a%5Bn-1%5D+-+1+ ALIGN=MIDDLE  ALT=\"+a%5Bn%5D+=+2a%5Bn-1%5D+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "——\r<BR>\n" );
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document.write( "To find the explicit formula, let's just do some substitutions on the first few values to see if it can be generalized:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5B1%5D+=+2a%5B0%5D+-+1+ ALIGN=MIDDLE  ALT=\"+a%5B1%5D+=+2a%5B0%5D+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5B2%5D+=+2a%5B1%5D+-+1+=+2%282a%5B0%5D+-+1%29+-+1+=+%282%5E2%29%2Aa%5B0%5D+-+2+-+1+ ALIGN=MIDDLE  ALT=\"+a%5B2%5D+=+2a%5B1%5D+-+1+=+2%282a%5B0%5D+-+1%29+-+1+=+%282%5E2%29%2Aa%5B0%5D+-+2+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5B3%5D+=+2a%5B2%5D+-+1+=+2%2A%282%5E2%2Aa%5B0%5D+-+2+-+1%29+-+1+=+%282%5E3%29a%5B0%5D+-+2%2A2+-+2+-+1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Those last three terms look a lot like  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5En+-+1+ ALIGN=MIDDLE  ALT=\"+2%5En+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (n=3 and the numbers add to 7)<BR>\n" );
document.write( "—\r<BR>\n" );
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document.write( "I claim that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5Bn%5D+=+%282%5En%29a%5B0%5D+-+%282%5En-1%29+ ALIGN=MIDDLE  ALT=\"+a%5Bn%5D+=+%282%5En%29a%5B0%5D+-+%282%5En-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "—\r<BR>\n" );
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document.write( "Check:    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5B4%5D+=+%282%5E4%29%283%2F2%29+-+%282%5E4-1%29+=+24+-+15+=+9+ ALIGN=MIDDLE  ALT=\"+a%5B4%5D+=+%282%5E4%29%283%2F2%29+-+%282%5E4-1%29+=+24+-+15+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (ok)\r<BR>\n" );
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