document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209373>Question 1209373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A geometric sequence has 400 terms.  The first term is 1600 and the common ratio is 9/10.  How many terms of this sequence are greater than 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848701 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The n-th term of the sequence is: a_n = 1600*(0.9)^(n-1)<BR>\n" );
document.write( "A term will be equal to 1 if 0.9^(n-1) = 1/1600<BR>\n" );
document.write( "To solve for n, we take the log of both sides:<BR>\n" );
document.write( "(n-1)log(0.9) = log(1/1600)<BR>\n" );
document.write( "n = log(1/1600)/log(0.9) + 1 = 71.02<BR>\n" );
document.write( "a_71 = 1600*0.9^70 = 1.0025<BR>\n" );
document.write( "a_72 = 1600*0.9^71 = 0.902<BR>\n" );
document.write( "Thus, the first 71 terms are greater than 1<BR>\n" );
document.write( " </SPAN>\n" );
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