document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134911>Question 1134911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively. (2 points)<BR>\n" );
document.write( "	<BR>\n" );
document.write( "an = 9 • 4n<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "an = 9 • (-4)n + 1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "an = 9 • 4n - 1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "an = 9 • (-4)n - 1<BR>\n" );
document.write( "5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752433 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Use \"^\" to denote exponentiation; and use parentheses where required.  The four answer choices should be<br><BR>\n" );
document.write( "a(n) = 9*4^n<BR>\n" );
document.write( "a(n) = 9*(-4)^(n+1)<BR>\n" );
document.write( "a(n) = 9*4^(n-1)<BR>\n" );
document.write( "a(n) = 9*(-4)^(n-1)<br><BR>\n" );
document.write( "The 2nd and 5th terms are opposite signs, so the common ratio has to be negative; so the first and third answer choices can't be right.<br><BR>\n" );
document.write( "The first term is -36.<br><BR>\n" );
document.write( "The second answer choice gives a(2) = 9*(-4)^3 = 9*-64 = -576.  not right.<BR>\n" );
document.write( "The fourth answer choice gives a(2) = 9*(-4)^1 = 9*(-4) = -36.  right.<br><BR>\n" );
document.write( "The problem is more educational if you aren't given answer choices....<br><BR>\n" );
document.write( "The 5th term 2304 is the 2nd term -36, multiplied by the common ratio 3 times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304%2F-36+=+-64+=+%28-4%29%5E3 ALIGN=MIDDLE  ALT=\"2304%2F-36+=+-64+=+%28-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  the common ratio is -4<br><BR>\n" );
document.write( "The 2nd term, -36, is the first term, multiplied by the common ratio once:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36+=+a%281%29%2A%28-4%29 ALIGN=MIDDLE  ALT=\"-36+=+a%281%29%2A%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29+=+%28-36%29%2F%28-4%29+=+9 ALIGN=MIDDLE  ALT=\"a%281%29+=+%28-36%29%2F%28-4%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  the first term is 9<br><BR>\n" );
document.write( "The n-th term is the first term, multiplied by the common ration (n-1) times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28n%29+=+%289%29%2A%28-4%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%28n%29+=+%289%29%2A%28-4%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "... which is the 4th answer choice </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );