document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092371>Question 1092371</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first difference of a sequence is the arithmetic sequence 3, 5, 7, 9, 11, ...... Find the first six terms of the original sequence in each of the following cases.\r<BR>\n" );
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document.write( "A. The first term in the original sequence is 3.<BR>\n" );
document.write( "B. The sum of the first two terms in the original sequence is 11.<BR>\n" );
document.write( "C. The fifth term in the original is 40. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707036 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=707036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>This should be pretty straightforward, if you understand what the first differences of a sequence mean.  The first differences being 3, 5, 7, 9, 11, ... means<BR>\n" );
document.write( "3 is the difference between the 1st and 2nd terms;<BR>\n" );
document.write( "5 is the difference between the 2nd and 3rd terms;<BR>\n" );
document.write( "7 is the difference between the 3rd and 4th terms;<BR>\n" );
document.write( "9 is the difference between the 4th and 5th terms; and<BR>\n" );
document.write( "11 is the difference between the 5th and 6th terms<br><BR>\n" );
document.write( "So....<BR>\n" );
document.write( "A. If the first term of the sequence is 3, then the 2nd is 3+3 = 6; the 3rd is 6+5 = 11; the 4th is 11+7 = 18; the 5th is 18+9 = 27, and the 6th is 27+11 = 38.<br><BR>\n" );
document.write( "B. If the sum of the first two terms is 11, and we know that the difference between the first two terms is 3, then we know the first two terms are 4 and 7.  To get the 3rd through 6th terms, simply add the given differences between terms, as demonstrated in part A.<br><BR>\n" );
document.write( "C. Given that the 5th term of the sequence is 40, you can find the 6th term by adding the known difference between the 5th and 6th terms; and you can find the 4th, 3rd, 2nd, and 1st terms by working backwards, subtracting the known differences between terms. <BR>\n" );
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