document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168724>Question 1168724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the formula an for the following sequences:<BR>\n" );
document.write( "1. 3, 4, 5, 6, 7,…<BR>\n" );
document.write( "2. 2, 5, 10, 17, 26,…<BR>\n" );
document.write( "3. √3, 3, 3√3, 9,…<BR>\n" );
document.write( "4. 4/1, 9/2, 16/3, 25/4,…<BR>\n" );
document.write( "5.  -  ½, 1/3, -1/4,… </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793353 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is of the form 3+(n-1)1 or more simply, (n+2). The differences are the same 1/1/1/1 so it is first power.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "this has differences of 3/5/7/9<BR>\n" );
document.write( "and they have differences of 2/2/2<BR>\n" );
document.write( "this makes it a quadratic<BR>\n" );
document.write( "n=1, value is 2<BR>\n" );
document.write( "so a(1)^2+b+c=2; a+b+c=2<BR>\n" );
document.write( "and 4a+2b+c=5<BR>\n" );
document.write( "and 9a+3b+c=10<BR>\n" );
document.write( "subtract second from third; first from second<BR>\n" );
document.write( "5a+b=5<BR>\n" );
document.write( "3a+b=3<BR>\n" );
document.write( "subtract second from first<BR>\n" );
document.write( "2a=2<BR>\n" );
document.write( "a=1, b=0<BR>\n" );
document.write( "so n^2 is first term and b=0, c=1<BR>\n" );
document.write( "(n^2+1) is the formula for an<BR>\n" );
document.write( "a4=17 a5=26 etc.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "This has a ratio of sqrt(3)<BR>\n" );
document.write( "a1=sqrt(3)^n=sqrt(3)<BR>\n" );
document.write( "a2=sqrt(3)^2=3, etc.<BR>\n" );
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document.write( "This has a ratio of 2^2/1; 3^2/2;  4^3/3, 5^2/4<BR>\n" );
document.write( "(n1+1)^2/n1<BR>\n" );
document.write( "-<BR>\n" );
document.write( "this has a -(1)/(n+1) form and the minus sign is first, matching the odd number.<BR>\n" );
document.write( "an=-1^(n)/(n+1); -1/2, 1/3, -1/4<BR>\n" );
document.write( " </SPAN>\n" );
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