document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123041>Question 1123041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of 5 consecutive integers is 505.\r<BR>\n" );
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document.write( "what is the third number in this sequence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739267 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=739267\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The quick answer given by tutor @ikleyn uses a shortcut that is often useful in problems involving arithmetic sequences.  (An arithmetic  sequence is a sequence of numbers in which there is a constant difference from one number to the next.  A sequence of consecutive integers is a common example.)<br><BR>\n" );
document.write( "Because of the equal spacing between the numbers in an arithmetic sequence, the middle number is the average of all the numbers.  In a sequence of 5 numbers, the 3rd number is the middle number.<br><BR>\n" );
document.write( "So in your problem the third number is the average of the 5 numbers -- which is the sum of the numbers, divided by how many there are: 505/5 = 101. </SPAN>\n" );
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