document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090885>Question 1090885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me?<BR>\n" );
document.write( "A sequence {g n} is defined recursively as g 1=72, g n=-2/3*g n-1 , for n &#8805;2\r<BR>\n" );
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document.write( "(note: here \"n\" & \"1\"& \"n-1\" after \"g\" should be a smaller letter, I cannot put it here as smaller)\r<BR>\n" );
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document.write( "a. Determine the values of g 2, g 3, and g 4<BR>\n" );
document.write( "b. Write an explicit formula for g n<BR>\n" );
document.write( "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 #705333 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D=72 ALIGN=MIDDLE  ALT=\"g%5B1%5D=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5Bn%5D=-%282%2F3%29%2Ag%5Bn-1%5D ALIGN=MIDDLE  ALT=\"g%5Bn%5D=-%282%2F3%29%2Ag%5Bn-1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28g%5Bn%5D=-%282%2F3%29%2Ag%5Bn-1%5D%2Cg%5B1%5D=72%29 ALIGN=MIDDLE  ALT=\"system%28g%5Bn%5D=-%282%2F3%29%2Ag%5Bn-1%5D%2Cg%5B1%5D=72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28g%5B2%5D=-%282%2F3%29%2Ag%5B1%5D%2Cg%5B3%5D=-%282%2F3%29%2Ag%5B2%5D%2Cg%5B4%5D=-%282%2F3%29%2Ag%5B3%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B2%5D=-%282%2F3%29%2A72 ALIGN=MIDDLE  ALT=\"g%5B2%5D=-%282%2F3%29%2A72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B2%5D=-2%2A72%2F3 ALIGN=MIDDLE  ALT=\"g%5B2%5D=-2%2A72%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28g%5B2%5D=-48%29 ALIGN=MIDDLE  ALT=\"highlight%28g%5B2%5D=-48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B3%5D=-%282%2F3%29%2A%28-48%29 ALIGN=MIDDLE  ALT=\"g%5B3%5D=-%282%2F3%29%2A%28-48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B3%5D=2%2A48%2F3 ALIGN=MIDDLE  ALT=\"g%5B3%5D=2%2A48%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28g%5B3%5D=32%29 ALIGN=MIDDLE  ALT=\"highlight%28g%5B3%5D=32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B4%5D=-%282%2F3%29%2A32 ALIGN=MIDDLE  ALT=\"g%5B4%5D=-%282%2F3%29%2A32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B4%5D=-2%2A32%2F3 ALIGN=MIDDLE  ALT=\"g%5B4%5D=-2%2A32%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28g%5B4%5D=-64%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28g%5B4%5D=-64%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5Bn%5D=g%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"g%5Bn%5D=g%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the general explicit formula for a geometric sequence  with first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D ALIGN=MIDDLE  ALT=\"g%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the sequence in this problem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28g%5Bn%5D=72%2A%28-2%2F3%29%5E%28n-1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28g%5Bn%5D=72%2A%28-2%2F3%29%5E%28n-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "That is \"an explicit formula\" for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5Bn%5D ALIGN=MIDDLE  ALT=\"g%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72=8%2A9=2%5E3%2A3%5E2 ALIGN=MIDDLE  ALT=\"72=8%2A9=2%5E3%2A3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the formula could be \"simplified\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5Bn%5D=72%2A%28-2%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"g%5Bn%5D=72%2A%28-2%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5Bn%5D=2%5E3%2A3%5E2%2A%28-1%29%5E%28n-1%29%2A2%5E%28n-1%29%2F3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"g%5Bn%5D=2%5E3%2A3%5E2%2A%28-1%29%5E%28n-1%29%2A2%5E%28n-1%29%2F3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28g%5Bn%5D=%28-1%29%5E%28n-1%29%2A2%5E%28n%2B2%29%2F3%5E%28n-3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28g%5Bn%5D=%28-1%29%5E%28n-1%29%2A2%5E%28n%2B2%29%2F3%5E%28n-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That last equation is also \"an explicit formula\" for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5Bn%5D ALIGN=MIDDLE  ALT=\"g%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As a formula it may not look simple,<BR>\n" );
document.write( "but it would help if you had to calculate several terms,<BR>\n" );
document.write( "because it would simplify calculations like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B4%5D=%28-1%29%5E3%2A2%5E6%2F3%5E1=-64%2F3 ALIGN=MIDDLE  ALT=\"g%5B4%5D=%28-1%29%5E3%2A2%5E6%2F3%5E1=-64%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B7%5D=%28-1%29%5E6%2A2%5E9%2F3%5E4=512%2F81 ALIGN=MIDDLE  ALT=\"g%5B7%5D=%28-1%29%5E6%2A2%5E9%2F3%5E4=512%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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