document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157621>Question 1157621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following problems completely and logically. <BR>\n" );
document.write( "Problem 1: Construct a difference table to determine the next term in the sequence<BR>\n" );
document.write( "17,15,25,53,105,18, ___.\r<BR>\n" );
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document.write( "Problem 2: Determine the nth-term formula for the number of square tiles<BR>\n" );
document.write( "in the nth figure. Then use this to find the number of square tiles<BR>\n" );
document.write( "in the 30th figure.<BR>\n" );
document.write( "a1=2squares, a2=4squares, a3=6squares, a4=8squares, a5=10squares\r<BR>\n" );
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document.write( "Problem 3: One straight cut across a pizza produces 2 pieces. Two cuts can produce a<BR>\n" );
document.write( "maximum of 4 pieces. Three cuts can produce a maximum of 7 pieces. Four cuts can produce<BR>\n" );
document.write( "a maximum of 11 pieces. Find the maximum number of pieces that can be produced </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780620 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=780620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Problem 1....<br><BR>\n" );
document.write( "I will ignore the last number in the sequence you show, since it is almost certainly a typo.<br><BR>\n" );
document.write( "(By the way, it would be polite of you to make sure the problem is correct before you post it....)<br><BR>\n" );
document.write( "So I will use the first five of the terms you show and use those to find the correct 6th term and the new 7th term.<br><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( "     17    15    25    53    105\r\n" );
document.write( "        -2    10    28    52\r\n" );
document.write( "           12    18    24\r\n" );
document.write( "               6     6</PRE><BR>\n" );
document.write( "The row of third differences is constant.  To find two more terms in the sequence, add two more 6's in that row and work back up the array.<br><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( "     17    15    25    53    105    187   305\r\n" );
document.write( "        -2    10    28    52     82    118\r\n" );
document.write( "           12    18    24     30    36\r\n" );
document.write( "               6     6     6     6</PRE><BR>\n" );
document.write( "ANSWERS: the correct 6th term is 187; the 7th term is 305.<br><BR>\n" );
document.write( "Problem 2....<br><BR>\n" );
document.write( "a1=2; a2=4; a3=6; a4=8; a5=10...<br><BR>\n" );
document.write( "Clearly the nth term is 2n; a30 = 60<br><BR>\n" );
document.write( "Problem 3....<br><BR>\n" );
document.write( "(Note your statement of the problem is not complete....)<br><BR>\n" );
document.write( "The numbers of regions for 1, 2, 3, and 4 cuts are<br><BR>\n" );
document.write( "2, 4, 7, 11<br><BR>\n" );
document.write( "Compare this sequence to the sequence of triangular numbers:<br><BR>\n" );
document.write( "1, 3, 6, 10<br><BR>\n" );
document.write( "The numbers in this sequence are each 1 more than the corresponding triangular number.<br><BR>\n" );
document.write( "The formula for the n-th triangular number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The formula for the maximum number of pieces of pizza with n cuts is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%29%2F2%2B1 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%29%2F2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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