document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018369>Question 1018369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Look at these 3 sequences along with possible answers<BR>\n" );
document.write( "for the next term. <BR>\n" );
document.write( "I am having the hardest time solving these patterns. <BR>\n" );
document.write( "What do you suggest?\r<BR>\n" );
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document.write( "1. 2,7,26,101,400? Answers; 1595, 800, 695, 1840\r<BR>\n" );
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document.write( "2*4-1 = 8-1 = 7<BR>\n" );
document.write( "7*4-2 = 28-2 = 26<BR>\n" );
document.write( "26*4-3 = 104-3 = 101<BR>\n" );
document.write( "101*4-4 = 404-4 = 400<BR>\n" );
document.write( "400*4-5 = 1600-5 = 1595  \r<BR>\n" );
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document.write( "2. 7, 21, 8, 72, 9? Answers; 81, 243, 123, 136\r<BR>\n" );
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document.write( "3. 7, 16, 8, 27, 9? Answers; 27, 10, 40, 37\r<BR>\n" );
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document.write( "Please help<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634551 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=634551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at these 3 sequences along with possible answers.<BR>\n" );
document.write( "I am having the hardest time solving these patterns.<BR>\n" );
document.write( "What do you suggest?\r<BR>\n" );
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document.write( "1. 2,7,26,101,400? Answers; 1595, 800, 695, 1840<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "This is how I did it.  You may have some other method.\r\n" );
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document.write( "I started out dividing each term by the preceding term\r\n" );
document.write( "to find out how much we're multiplying by each time to\r\n" );
document.write( "get the next term.\r\n" );
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document.write( "7/2 = 3 1/2\r\n" );
document.write( "26/7 = 3 5/7\r\n" );
document.write( "101/26 = 3 23/26\r\n" );
document.write( "400/101 = 3 97/101\r\n" );
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document.write( "Looking at those numbers shows that they're getting \r\n" );
document.write( "closer and closer to multiplying by 4.\r\n" );
document.write( "So I asked myself, How much less is it each time\r\n" );
document.write( "than multiplying by 4?  So I investigated this way:\r\n" );
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document.write( "2*4 = 8.  The next term, 7, is 1 less than 8.\r\n" );
document.write( "7*4 = 28.  The next term, 26, is 2 less than 28.\r\n" );
document.write( "26*4 = 104.  The next term, 101, is 3 less than 104.\r\n" );
document.write( "101*4 = 404.  The next term, 400, is 4 less than 404. \r\n" );
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document.write( "From that I got the pattern\r\n" );
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document.write( "2*4-1 = 8-1 = 7\r\n" );
document.write( "7*4-2 = 28-2 = 26\r\n" );
document.write( "26*4-3 = 104-3 = 101\r\n" );
document.write( "101*4-4 = 404-4 = 400\r\n" );
document.write( "400*4-5 = 1600-5 = 1595  \r\n" );
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document.write( "</PRE><BR>\n" );
document.write( "2. 7, 21, 8, 72, 9? Answers; 81, 243, 123, 136<BR>\n" );
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document.write( "I noticed that the 1st, 3rd and 5th terms formed\r\n" );
document.write( "the pattern 7,8,9\r\n" );
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document.write( "Then I noticed that 21 was 7*3 and 72 was 8*9\r\n" );
document.write( "and that 3 is 3 to the 1 power and 9 is 3 to the 2 power.\r\n" );
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document.write( "7\r\n" );
document.write( "7*3<sup>1</sup> = 7*3 = 21\r\n" );
document.write( "8\r\n" );
document.write( "8*3<sup>2</sup> = 8*8 = 72\r\n" );
document.write( "9\r\n" );
document.write( "9*3<sup>3</sup> = 9*27 = 243\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "3. 7, 16, 8, 27, 9? Answers; 27, 10, 40, 37<BR>\n" );
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document.write( "This one is similar to the previous one.\r\n" );
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document.write( "I noticed that the 1st, 3rd and 5th terms formed\r\n" );
document.write( "the pattern 7,8,9\r\n" );
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document.write( "Then I noticed that 16 was 2 more than multiplying\r\n" );
document.write( "7 by 2.\r\n" );
document.write( "Then I noticed that 27 was 3 more than multiplying\r\n" );
document.write( "8 by 3\r\n" );
document.write( "So I figured that the next term after 9 would be 4 more than\r\n" );
document.write( "multiplying 9 by 4.  That would be 4 more than 36 or 40\r\n" );
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document.write( "7\r\n" );
document.write( "7*2 = 14, 14+2 = 16\r\n" );
document.write( "8\r\n" );
document.write( "8*3 = 24, 24+3 = 27\r\n" );
document.write( "9\r\n" );
document.write( "9*4 = 36, 36+4 = 40\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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