document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388620>Question 388620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4 A recurrance relationship is such that Un+1=a/4Un+12. <BR>\n" );
document.write( "4(a).If U0=16 show clearly that U2=aČ+3a+12 <BR>\n" );
document.write( "4(b).Hence find a if U2=30 and a>0\r<BR>\n" );
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document.write( "Can you provide full working with solution.\r<BR>\n" );
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document.write( "Many Thanks,<BR>\n" );
document.write( "Andy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275059 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=275059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> U<sub>n+1</sub> = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2F4%29%2AU%5Bn%5D+%2B+12 ALIGN=MIDDLE  ALT=\"%28a%2F4%29%2AU%5Bn%5D+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B0%5D+=+16 ALIGN=MIDDLE  ALT=\"U%5B0%5D+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > show clearly that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D+=+a%5E2+%2B+3x+%2B+12 ALIGN=MIDDLE  ALT=\"U%5B2%5D+=+a%5E2+%2B+3x+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B0%5D ALIGN=MIDDLE  ALT=\"U%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation above we can find find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B1%5D ALIGN=MIDDLE  ALT=\"U%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then use that to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D ALIGN=MIDDLE  ALT=\"U%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We start with n = 0:<BR>\n" );
document.write( "U<sub>0+1</sub> = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2F4%29%2AU%5B0%5D+%2B+12 ALIGN=MIDDLE  ALT=\"%28a%2F4%29%2AU%5B0%5D+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B1%5D+=+%28a%2F4%29%2A%2816%29+%2B+12 ALIGN=MIDDLE  ALT=\"U%5B1%5D+=+%28a%2F4%29%2A%2816%29+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B1%5D+=+4a+%2B+12 ALIGN=MIDDLE  ALT=\"U%5B1%5D+=+4a+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we use n = 1:<BR>\n" );
document.write( "U<sub>1+1</sub> = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2F4%29%2AU%5B1%5D+%2B+12 ALIGN=MIDDLE  ALT=\"%28a%2F4%29%2AU%5B1%5D+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "U<sub>1+1</sub> = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2F4%29%2A%284a+%2B+12%29+%2B+12 ALIGN=MIDDLE  ALT=\"%28a%2F4%29%2A%284a+%2B+12%29+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note the use of parentheses. It is an extremely good habit to use parentheses when replacing one expression with another one. With the parentheses it is clear that we must use the Distributive Property to multiply correctly:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D+=+%28a%2F4%29%2A%284a%29+%2B+%28a%2F4%29%2A%2812%29+%2B+12 ALIGN=MIDDLE  ALT=\"U%5B2%5D+=+%28a%2F4%29%2A%284a%29+%2B+%28a%2F4%29%2A%2812%29+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D+=+a%5E2+%2B+3a+%2B+12 ALIGN=MIDDLE  ALT=\"U%5B2%5D+=+a%5E2+%2B+3a+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b. Find a if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D+=+30 ALIGN=MIDDLE  ALT=\"U%5B2%5D+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a > 0:<BR>\n" );
document.write( "Using the equation we got for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D ALIGN=MIDDLE  ALT=\"U%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D ALIGN=MIDDLE  ALT=\"U%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > with 30:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5B2%5D+=+a%5E2+%2B+3a+%2B+12 ALIGN=MIDDLE  ALT=\"U%5B2%5D+=+a%5E2+%2B+3a+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+a%5E2+%2B+3a+%2B+12 ALIGN=MIDDLE  ALT=\"30+=+a%5E2+%2B+3a+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can solve for a. This is a quadratic equation so we want one side to be zero. Subtracting 30 from each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+a%5E2+%2B+3a+-+18 ALIGN=MIDDLE  ALT=\"0+=+a%5E2+%2B+3a+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we either factor or use the Quadratic Formula. This factors easily:<BR>\n" );
document.write( "(a+6)(a-3) = 0<BR>\n" );
document.write( "From the Zero Product Property we know that this (or any) product can be zero <i>only</i> if one (or more) of the factors is zero. So:<BR>\n" );
document.write( "a+6 = 0 or a-3 = 0<BR>\n" );
document.write( "Solving these we get:<BR>\n" );
document.write( "a = -6 or a = 3<BR>\n" );
document.write( "Since we were told that a > 0 we must reject the a = -6 solution. So a = 3. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );