document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195915>Question 1195915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> First number sequence:<BR>\n" );
document.write( "75,15,25,5,15, ...\r<BR>\n" );
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document.write( "The correct next number is 3<BR>\n" );
document.write( "I don't get why?\r<BR>\n" );
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document.write( "Second sequence:<BR>\n" );
document.write( "183 305 527 749 961 ...\r<BR>\n" );
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document.write( " The correct next number is 293.<BR>\n" );
document.write( "I also can't solve it.\r<BR>\n" );
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document.write( "Please help to understand how they both work? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828541 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There is no formal mathematics involved in finding the answer to ANY problems like these.  As one of the tutors says in his response, finding AN answer is matter of trial and error, and of luck.<br><BR>\n" );
document.write( "And it is ABSURD for the statement of the problem to say what the \"correct\" next numbers are.  It is undoubtedly true that those next numbers are \"correct\" IF YOU USE THE SAME RULE AS THE PERSON WHO CREATED THE PROBLEM; however, in ANY such problem, ANY next number will form a valid sequence.<br><BR>\n" );
document.write( "For the first example, the repeated rule \"divide by 5; add 10\" is VERY LIKELY the answer according to the creator of the problem.  However, it CANNOT be said that the next number obtained using that rule is THE correct answer.<br><BR>\n" );
document.write( "For the second example, one of the tutors uses an argument for how to find that the \"correct\" next number is 293; however, his rule is not completely consistent.<br><BR>\n" );
document.write( "Using his basic idea, I see a different pattern, leading to a different next number:<BR>\n" );
document.write( "The first digits of the given numbers are 1, 3, 5, 7, 9; so the first digit of the next number should again be 1.<BR>\n" );
document.write( "The second digits of the given numbers are 8,0,2,4,6; so the second digit of the next number should again be 8.<BR>\n" );
document.write( "The third digits of the given numbers are 3, 5, 7, 9, 1; so the third digit of the next number should again be 3.<br><BR>\n" );
document.write( "So the next number should be 183, not 293.<br><BR>\n" );
document.write( "So I obtain a next number that is different than the given \"correct\" answer, using a pattern that is more consistent than the pattern used by the other tutor to match the given \"correct\" answer.<br><BR>\n" );
document.write( "So is my answer right, and the \"correct\" answer given in the statement of the problem is wrong?<br><BR>\n" );
document.write( "Of course we can't say that.  The problem -- like ALL other similar problems -- is fatally flawed; given ONLY a sequence of numbers without any context, it is ALWAYS IMPOSSIBLE to know what any other numbers in the sequence are.<br><BR>\n" );
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