document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=853272>Question 853272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the 10th term of the sequence 64, 16, 4,...?\r<BR>\n" );
document.write( "\n" );
document.write( "a. 1/2024<BR>\n" );
document.write( "b. 1/256<BR>\n" );
document.write( "c. 1/4096<BR>\n" );
document.write( "d. 1/496 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513991 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=513991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the type of sequence.  This is a geometric sequence with a common term of 1/4, because each term * 1/4 is the next term.<P><BR>\n" );
document.write( "For any geometric sequence, the nth term = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29+%2A+r%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%281%29+%2A+r%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a(1) is the first term, n is the term number you're trying to find, and r is the common ratio.<P><BR>\n" );
document.write( "Let's test it with the third term.  The third term = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A%281%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"64%2A%281%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64/16 = 4.  That is the third term.  See, it works!<P><BR>\n" );
document.write( "The tenth term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A%281%2F4%29%5E9 ALIGN=MIDDLE  ALT=\"64%2A%281%2F4%29%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64/262144 = 1/4096.  The answer is c.<P><BR>\n" );
document.write( "If you didn't remember the formula, write out the terms, dividing each subsequent term by 4 (which is multiplying it by 1/4), until you reach the 10th term.<P><BR>\n" );
document.write( "64, 64/4=16, 16/4=4, 4/4=1, 1/4=1/4, 1/4 / 4 = 1/16, 1/16 / 4 = 1/64, 1/64 / 4 = 1/256, 1/256/4 = 1/1024, 1/1024 / 4 = 1/4096. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );