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 #828537 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=828537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Question 1\r<BR>\n" );
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document.write( "For problems like this, we basically involve trial and error. There is no single approach. Effectively we have to get lucky to guess the pattern most of the time. With more practice, it should come easier.\r<BR>\n" );
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document.write( "The jump from 75 to 15 is \"divide by 5\" since<BR>\n" );
document.write( "75/5 = 15\r<BR>\n" );
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document.write( "To get from 15 to 25, we add 10<BR>\n" );
document.write( "15+10 = 25\r<BR>\n" );
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document.write( "Then from 25 to 5 is another \"divide by 5\" operation.<BR>\n" );
document.write( "25/5 = 5\r<BR>\n" );
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document.write( "The pattern goes: \"divide by 5, add 10, divide by 5, add 10\" and so on.\r<BR>\n" );
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document.write( "Divide: 75/5 = 15<BR>\n" );
document.write( "Add: 15+10 = 25<BR>\n" );
document.write( "Divide: 25/5 = 5<BR>\n" );
document.write( "Add: 5+10 = 15<BR>\n" );
document.write( "Divide: 15/5 = 3\r<BR>\n" );
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document.write( "Keep in mind that sequence problems like this are fundamentally flawed. <BR>\n" );
document.write( "Why is that? <BR>\n" );
document.write( "Check out my previous response on <a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1195799.html\">this page</a> for more information.<BR>\n" );
document.write( "The summary of what I mention is that the sequence 1,2,4 could have infinitely many possible numbers as the fourth term; questions that ask about the next term are often too vague to answer. Further context is needed. \r<BR>\n" );
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document.write( "Question 2\r<BR>\n" );
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document.write( "This is another \"think outside the box\" type of question. <BR>\n" );
document.write( "The approach is far from obvious.\r<BR>\n" );
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document.write( "The idea is to add 2 to each digit<BR>\n" );
document.write( "183 breaks up into 1, 8, 3<BR>\n" );
document.write( "Adding 2 to each gets:<BR>\n" );
document.write( "1+2 = 3<BR>\n" );
document.write( "8+2 = 10<BR>\n" );
document.write( "3+2 = 5\r<BR>\n" );
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document.write( "So the 1,8,3 becomes 3,10,5<BR>\n" );
document.write( "If we drop the tens digit \"1\" from \"10\", then we now have 3,0,5 hence the second term 305\r<BR>\n" );
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document.write( "Now let's repeat the process of adding 2 to each digit<BR>\n" );
document.write( "3+2 = 5<BR>\n" );
document.write( "0+2 = 2<BR>\n" );
document.write( "5+2 = 7<BR>\n" );
document.write( "It matches with the 527 as the third term. So far, so good.\r<BR>\n" );
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document.write( "Repeat again:<BR>\n" );
document.write( "5+2 = 7<BR>\n" );
document.write( "2+2 = 4<BR>\n" );
document.write( "7+2 = 9<BR>\n" );
document.write( "This matches as well.\r<BR>\n" );
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document.write( "And,<BR>\n" );
document.write( "7+2 = 9<BR>\n" );
document.write( "4+2 = 6<BR>\n" );
document.write( "9+2 = 11<BR>\n" );
document.write( "We drop the tens digit of \"11\" to be left with \"1\"<BR>\n" );
document.write( "So we land on 961\r<BR>\n" );
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document.write( "Repeat one final time<BR>\n" );
document.write( "9+2 = 11<BR>\n" );
document.write( "6+2 = 8<BR>\n" );
document.write( "1+2 = 3<BR>\n" );
document.write( "We arrive at 183 (not 293)<BR>\n" );
document.write( "The terms of the sequence will loop at this point since we arrived at one of the values previously mentioned.\r<BR>\n" );
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document.write( "Like with question 1, there are likely infinitely many ways we could generate the original sequence of {183, 305, 527, 749, 961}, which may or may not lead to 183 or 293 as the next term (or perhaps any number really). <BR>\n" );
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