document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212860>Question 212860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the solution to this input output problem?                                                                                                                                                        E   P<BR>\n" );
document.write( "1   3<BR>\n" );
document.write( "2   5<BR>\n" );
document.write( "3   9<BR>\n" );
document.write( "4  17<BR>\n" );
document.write( "5  33                                                                            </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160840 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=160840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Most of these type problems are practice. I like to start by looking at the series of numbers. You can see the difference in the inputs goes up by 1 one each entry. Now look and see if you can find a pattern in the output numbers.\r<BR>\n" );
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document.write( "You can see they are getting larger by increasingly larger amounts. However, nothing obvious jumps out a bout their values. So, the first thing I like to try is to see if there are patterns in the series of outputs. For instance, perhaps every other number has an obvious pattern.  One thing I always try is finding the difference between each successive output number.<BR>\n" );
document.write( "difference between 5 and 3 = 2<BR>\n" );
document.write( "difference between 9 and 5 = 4<BR>\n" );
document.write( "difference between 17 and 9 = 8   do you see the pattern yet<BR>\n" );
document.write( "difference between 33 and 17 = 16  \r<BR>\n" );
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document.write( "So each output increases by a value that is power of 2. Now all that is left to figure out is what the 'starting' value is. A little trail and error will show you that value is 1.<BR>\n" );
document.write( "So, the function that fits the given data points is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+1+%2B+2%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29+=+1+%2B+2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > x>=1 </SPAN>\n" );
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