document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309476>Question 309476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is: <BR>\n" );
document.write( "The nth term of a sequence is 4/n^2<BR>\n" );
document.write( "(a)Write down the first three terms of the sequence, expressing each term in its simplest form.\r<BR>\n" );
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document.write( "(b)The kth term in the sequence is 1/100<BR>\n" );
document.write( "Find the value of k<BR>\n" );
document.write( "Note: it is K not N\r<BR>\n" );
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document.write( "(c)Given that the nth term of the sequence is less than 0.0064, find the smallest value of n. '\r<BR>\n" );
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document.write( "I shall be highly glad if you help me.<BR>\n" );
document.write( "Regards,<BR>\n" );
document.write( "Benjamin. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221396 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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=221396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "n = 1 -> 4/1^2 = 4/1 = 4 <BR>\n" );
document.write( "n = 2 -> 4/2^2 = 4/4 = 1 <BR>\n" );
document.write( "n = 3 -> 4/3^2 = 4/9  \r<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "n = k -> 4/k^2 = 1/100<BR>\n" );
document.write( "4*100 = k^2<BR>\n" );
document.write( "400 = k^2<BR>\n" );
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document.write( "k = 20\r<BR>\n" );
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document.write( "(c) <BR>\n" );
document.write( "4/n^2 < 0.0064<BR>\n" );
document.write( "4/0.0064 < n^2<BR>\n" );
document.write( "625 < n^2<BR>\n" );
document.write( "0 < n^2 - 625<BR>\n" );
document.write( "0 < (n - 25)*(n + 25)<BR>\n" );
document.write( "n = 25 or n = -25\r<BR>\n" );
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document.write( "++ -- ++<BR>\n" );
document.write( "--o--o---<BR>\n" );
document.write( "-25  25<BR>\n" );
document.write( "*if n = 0 then 0^2 - 625 = -625 -> it gives the negative result for n = 0<BR>\n" );
document.write( "because n = 0 is between -25 and 25, so the area between -25 and 25 will give negative result for the equation, and the left side and the right side of that area will give positive result<BR>\n" );
document.write( "*because the equation should make result that is greater than 0 (>0) so the solution set for that inequality is the area that gives positive result.<BR>\n" );
document.write( "so, n < -25 or n > 25\r<BR>\n" );
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document.write( "because n should not be negative number, the smallest value of n so that the nth term of the sequence is less than 0.0064 is 26 (the first integer that is greater than 25) </SPAN>\n" );
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