document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=240496>Question 240496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can you know how many number there are in a given sequence?<BR>\n" );
document.write( "For example from 1 to 100, there are 100 numbers<BR>\n" );
document.write( "From 100 to 1000 there are 901 numbers(I know because my teacher tells me)<BR>\n" );
document.write( "How can you know right away how many numbers there are?\r<BR>\n" );
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document.write( "Please explain a little bit carefully! Thanks for your helps! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176219 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=176219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, the formula is: last - first + 1.<br><BR>\n" );
document.write( "To understand this, let's look at the example you gave: How many numbers from 100 to 1000?<ul><li>First, how many numbers are there from 1 to 1000? Clearly (I hope) there are 1000 numbers.</li><li>Of the numbers from 1 to 1000, which ones are <b>not</b> included in the numbers from 100 to 1000? Again I hope it is clear that 1 through 99 are not included.</li><li>The number of numbers from 100 to 1000 would be the number of numbers of 1 to 1000 minus the number of numbers from 1 to 99: 1000 - 99 = 901.</li></ul><BR>\n" );
document.write( "Let's look at a general case. Let L = the last (or highest number) and F = the first (or lowest number in the sequence. That makes (F-1) the highest number that is not in the sequence.<br><BR>\n" );
document.write( "Therefore the  number of numbers in the sequence will be: the number of numbers from 1 to L (which is L) minus the number of numbers from 1 to (F-1) (which is (F-1):<BR>\n" );
document.write( "L - (F-1) = L - F + 1<BR>\n" );
document.write( "which is the formula I gave you at the beginning.<br><BR>\n" );
document.write( "Here's an example: How many numbers are there from 536 to 2349? Answer: 2349 - 536 + 1 = 1814<br><BR>\n" );
document.write( "I hope this helps. </SPAN>\n" );
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