document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=342107>Question 342107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you go about finding a pattern in a sequence of numbers? i just keep trying out different numbers but i just sit there for hours and some times i still don't see a pattern. Is there a process for finding a pattern? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244864 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=244864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  How do you go about finding a pattern in a sequence of numbers? i just keep trying out different numbers but i just sit there for hours and some times i still don't see a pattern. Is there a process for finding a pattern?<BR>\n" );
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document.write( "Assume you have a geometric sequence: 1,2,4,8,16,32,,,<BR>\n" );
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document.write( "You are looking for a pattern to describe a(n) which is the nth term.<BR>\n" );
document.write( "Start with<BR>\n" );
document.write( "a(1) = 1<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Now a(2) is 2 but you are interested in finding the pattern<BR>\n" );
document.write( "so you write<BR>\n" );
document.write( "a(2) = 2*a(1)<BR>\n" );
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document.write( "Now a(3) is 4 but you are interested in finding the pattern<BR>\n" );
document.write( "so you write<BR>\n" );
document.write( "a(3) = 2*a(2) = 2*2*a(1) = 2^2*a(1)<BR>\n" );
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document.write( "Notice how you try to describe later numbers as related to an earlier number.<BR>\n" );
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document.write( "a(4) = 2^3*a(1)<BR>\n" );
document.write( "....<BR>\n" );
document.write( "Keep this up as long as you have to till you see a pattern.<BR>\n" );
document.write( "a(n) = 2^(n-1)*a(1)<BR>\n" );
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document.write( "Now, a(1) is 1 in this problem so you can drop that<BR>\n" );
document.write( "a(n) = 2^(n-1)<BR>\n" );
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document.write( "Note: A sequence is a function with domain = 1,2,3,4,...,n<BR>\n" );
document.write( "You are looking for a Rule for this function.<BR>\n" );
document.write( "The Rule has to describe the y-value when n = 1 or 2 or 3, or simply n.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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