document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3709>Question 3709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a very hard time understanding college algebra. Can anyone help me solve these problems.\r<BR>\n" );
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document.write( "The first 3 problems have to do with sequences. <BR>\n" );
document.write( "1.  5,3,7,1,9,-1     Find a9 then find sum of 9\r<BR>\n" );
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document.write( "2.  12,9,6,   What is 25n, and what is sum of 25 (s25)\r<BR>\n" );
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document.write( "3.  4,8,16   Find a12 and find sum of 12 (s12)\r<BR>\n" );
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document.write( "4.  (x+y)^7   Expand\r<BR>\n" );
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document.write( "5. (2x+3y)^4  Expand\r<BR>\n" );
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document.write( "6.  (3x-2y)^5  Expand  On this last one he gave us a hint but i do not understand. (x-y)=[(x)+(-y)] Can anyone please help!!!!!!!!!!!!!!!!!!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1644 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=1644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I only solve the questions about seq. \r<BR>\n" );
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document.write( " 1.  5,3,7,1,9,-1     Find a9 then find sum of 9<BR>\n" );
document.write( "     Sol: a1 =5, a2 = a1-2, a3=a2+4,a4=a3-6,a5=a4+8,...<BR>\n" );
document.write( "          In general, we see that an= a(n-1)+ (-1)^(n-1) 2(n-1) for n >= 2.<BR>\n" );
document.write( "          And,so a7 = -1 + 2*6 = 11,  a8 = 11 - 2*7 = -3.<BR>\n" );
document.write( "          Hence, a9 = -3 + 2*8 = 13.<BR>\n" );
document.write( "          s9 = s1+s2+...+a9 = 5+3+7+1+9-1+11-3+13 = 25 + 24 - 4 = 45.<BR>\n" );
document.write( "          In general , sn = a1* n = 5n if n is odd.<BR>\n" );
document.write( "           and s2n = 10n - 2*n for n >= 1.\r<BR>\n" );
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document.write( "2.  12,9,6,   What is 25n, and what is sum of 25 (s25)<BR>\n" );
document.write( "    Sol: This is an arithmetic seq with common difference -3.<BR>\n" );
document.write( "         an= an-1 -3, so an = a1 + (n-1)(-3) = 15 -3n. <BR>\n" );
document.write( "         So, a25 = 15 -3*25 = -60.<BR>\n" );
document.write( "         Also sn =  n(a1+an)/2 = n(27 - 3n)/2 = 27n/2 -3n^2/2.<BR>\n" );
document.write( "         So, s25 = (27*25 - 3*25^2)/2 = -600         \r<BR>\n" );
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document.write( " 3.  4,8,16   Find a12 and find sum of 12 (s12)<BR>\n" );
document.write( "    Sol: This is a geometric seq with common ratio 2.<BR>\n" );
document.write( "         an= 2an, so an = a1*2^(n-1) = 4* 2^(n-1) for n>=1.<BR>\n" );
document.write( "         And, sn = a1(1-r^n)/(1-r) = 4(2^n-1) .<BR>\n" );
document.write( "         We get a12 = 4*2^11 = 8*1024 = 8192.<BR>\n" );
document.write( "         and s12 = 4(2^12 -1) = 16380.\r<BR>\n" );
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document.write( " The rest concerning binomial formula , should be staightforward.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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