document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167598>Question 1167598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let <BR>\n" );
document.write( "b0, b1, b2, be the sequence defined by the explicit formula<BR>\n" );
document.write( "bn = C · 5^n + D(−4)^n for each integer n ≥ 0,<BR>\n" );
document.write( "where C and D are real numbers.<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "Find C and D so that <BR>\n" );
document.write( "b0 = 0<BR>\n" );
document.write( " and <BR>\n" );
document.write( "b1 = −9.\r<BR>\n" );
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document.write( "b) Find C and D so that <BR>\n" );
document.write( "b0 = 4<BR>\n" );
document.write( " and <BR>\n" );
document.write( "b1 = 11.\r<BR>\n" );
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document.write( "c)What is <BR>\n" );
document.write( "b2 in this case? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852196 by </B><A HREF=/tutors/aboutme.mpl?userid=Resolver123><B>Resolver123(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Resolver123><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=852196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D+=+c%2A5%5En+%2B+d%2A%28-4%29%5En ALIGN=MIDDLE  ALT=\"b%5Bn%5D+=+c%2A5%5En+%2B+d%2A%28-4%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E=0 ALIGN=MIDDLE  ALT=\"n%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B0%5D+=+c%2A5%5E0+%2B+d%2A%28-4%29%5E0=c%2Bd=0 ALIGN=MIDDLE  ALT=\"b%5B0%5D+=+c%2A5%5E0+%2B+d%2A%28-4%29%5E0=c%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, by hypothesis, after direct substitution.<BR>\n" );
document.write( "Also, inserting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the formula gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D+=+c%2A5%5E1+%2B+d%2A%28-4%29%5E1=-9 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+c%2A5%5E1+%2B+d%2A%28-4%29%5E1=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5c-4d=-9 ALIGN=MIDDLE  ALT=\"5c-4d=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "From c + d = 0, we get d = -c. <BR>\n" );
document.write( "Substituting this into the equation 5c - 4d = -9 gives 5c - 4(-c) = 5c+4c = -9,<BR>\n" );
document.write( "or 9c = -9, or c = -1. <BR>\n" );
document.write( "Therefore, c = -1, and d = -(-1) = 1.\r<BR>\n" );
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document.write( "(b) Similarly, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D+=+c%2A5%5En+%2B+d%2A%28-4%29%5En ALIGN=MIDDLE  ALT=\"b%5Bn%5D+=+c%2A5%5En+%2B+d%2A%28-4%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B0%5D+=+c%2A5%5E0+%2B+d%2A%28-4%29%5E0=c%2Bd=4 ALIGN=MIDDLE  ALT=\"b%5B0%5D+=+c%2A5%5E0+%2B+d%2A%28-4%29%5E0=c%2Bd=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or c + d = 4, or d = 4 - c. Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D+=+c%2A5%5E1+%2B+d%2A%28-4%29%5E1=11 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+c%2A5%5E1+%2B+d%2A%28-4%29%5E1=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 5c - 4d = 11.\r<BR>\n" );
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document.write( "Substituting, 5c - 4(4 - c) = 11, or 5c - 16 + 4c = 11.<BR>\n" );
document.write( "This gives 9c = 27, or c = 3, which consequently gives d = 4 - 3 = 1.\r<BR>\n" );
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document.write( "(c) From part (b), we get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D+=+3%2A5%5En+%2B+%28-4%29%5En ALIGN=MIDDLE  ALT=\"b%5Bn%5D+=+3%2A5%5En+%2B+%28-4%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D+=+3%2A5%5E2+%2B+%28-4%29%5E2=3%2A25%2B16+=+75%2B16=91 ALIGN=MIDDLE  ALT=\"b%5B2%5D+=+3%2A5%5E2+%2B+%28-4%29%5E2=3%2A25%2B16+=+75%2B16=91\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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