document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31731>Question 31731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem is to find the general equation for the sequence, {-1,3,-5,7,-9,11,-13,15...}.  I know that -1+4=3;-1-4=-5; -1+8=7;-1-8=-9; etc...so I am guessing it involves 4*n since the difference between the numbers is 4,8,12,16,20,24,28 respectively.  Also, the alternating signs indicate -1^n. I also wondered if it involved absolute value. I just haven't been able to put it together with the formula for an arithmetic sequence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18339 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem is to find the general equation for the sequence, {-1,3,-5,7,-9,11,-13,15...}.  I know that -1+4=3;-1-4=-5; -1+8=7;-1-8=-9; etc...so I am guessing it involves 4*n since the difference between the numbers is 4,8,12,16,20,24,28 respectively.  Also, the alternating signs indicate -1^n. I also wondered if it involved absolute value. I just haven't been able to put it together with the formula for an arithmetic sequence.<BR>\n" );
document.write( "YOU ARE ON RIGHT TRACK...THIS IS AN ALTERNATING SEQUENCE WITH 2 FORMULAE FOR N TH.<BR>\n" );
document.write( "TERMS<BR>\n" );
document.write( "ODD TERMS ARE .....-1,-5,-9,-13....ETC<BR>\n" );
document.write( "SO A=-1,CD=-5+1=-4.....SO TM FOR THIS IS TM=-1-4(M-1)=-1-4M+4=3-4M....WE USED M HERE INSTEAD OF CONVENTIONAL N WHICH IS RESEVED FOR THE ORIGINAL SERIES<BR>\n" );
document.write( "SO WHEN N IS ODD OR FOR T(2N-1)..THIS IS THE FORMULA<BR>\n" );
document.write( "T(2N-1)=3-4N<BR>\n" );
document.write( "NOW EVEN TERMS ARE...3,7,11,15.......ETC....BUT THESE ARE STARTING FROM SECOND TERM IN THE SERIES<BR>\n" );
document.write( "SO A=3,CD=4...........TR=3+4(R-1)=4R-1<BR>\n" );
document.write( "SO WHEN N IS EVEN WE HAVE ...FOR T2N...THIS IS THE FORMULA<BR>\n" );
document.write( "T2N=4N-1..................<BR>\n" );
document.write( "THUS THE SERIES IS DEFINED BY 2 FORMULAE(LIKE WE DO FOR FUNCTIONS IN DIFFERENT RANGES)<BR>\n" );
document.write( "T(2N-1)=3-4N AND T2N=4N-1. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );