document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182732>Question 1182732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Start with the number 1 and create the sequence:<BR>\n" );
document.write( "1,2,4,8,16,22,24,28<BR>\n" );
document.write( "where each number is the sum of the previous number and its final digit. How many numbers in the sequence are less than 1000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812825 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=812825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Write out the next 10-20 numbers in the sequence....<BR>\n" );
document.write( "1, 2, 4, 8, 16, 22, 24, 28, 36, 42, 44, 48, 56, 62, 64, 68, 76, 82, 84, 88, 96, ...<br><BR>\n" );
document.write( "... and look for a pattern:<BR>\n" );
document.write( "1, 2, 4, 8, 16 // 22, 24, 28, 36 // 42, 44, 48, 56 // 62, 64, 68, 76 // 82, 84, 88, 96 // ...<br> <BR>\n" );
document.write( "5 numbers less than 19<BR>\n" );
document.write( "4 more numbers 20 to 39<BR>\n" );
document.write( "4 more number 40 to 59<BR>\n" );
document.write( "4 more numbers 60 to 79<BR>\n" );
document.write( "4 more numbers 80 to 99<BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "It should be clear that the pattern will continue.<br><BR>\n" );
document.write( "There are 4 numbers in the sequence in every interval of 20 consecutive integers, except there is 1 additional number in the sequence among the first 20 integers.<br><BR>\n" );
document.write( "The number of intervals of length 20 up to 1000 is 1000/20 = 50; so<br><BR>\n" );
document.write( "ANSWER: the number of numbers in the sequence less than 1000 is 50(4)+1 = 201.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );