document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038745>Question 1038745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653459 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=653459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A2 = 17<BR>\n" );
document.write( "A5 = 19<BR>\n" );
document.write( "A5 - A2 = 2<BR>\n" );
document.write( "5 - 2 = 3<BR>\n" );
document.write( "average difference is 2/3.<BR>\n" );
document.write( "since this is an arithmetic sequence, it has to be the common difference.\r<BR>\n" );
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document.write( "the formula for an arithmetic sequence is An = A1 + (n-1)*d<BR>\n" );
document.write( "An is the nth term.<BR>\n" );
document.write( "A1 is the first term.<BR>\n" );
document.write( "d is the common difference.\r<BR>\n" );
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document.write( "A2 is therefore equal to A1 + 1 * 2/3 because 2 minus 1 is equal to 1 and the common difference is equal to 2/3.<BR>\n" );
document.write( "since A2 is equal to 17, you get 17 = A1 + 2/3.<BR>\n" );
document.write( "solve for A1 to get A1 = 16 and 1/3.\r<BR>\n" );
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document.write( "using the same formula, if A1 is correct and d is correct, A5 should be equal to 16 and 1/3 + 4*2/3 which would make it equal to 16 and 1/3 + 8/3 which would make it equal to 16 and 9/3 which makes it equal to 16 and 3 which make it equal to 19.\r<BR>\n" );
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document.write( "looks like the formula works and the common difference is 2/3 and the first term is 16 and 1/3.\r<BR>\n" );
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document.write( "the eighth term would be A8.<BR>\n" );
document.write( "based on the formula A8 = 16 and 1/3 + 7*2/3 which becomes A8 = 16 and 1/3 + 14/3 which becomes A8 = 16 and 15/3 which becomes A8 = 16 and 5 which makes A8 equal to 21.\r<BR>\n" );
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document.write( "start with A5 = 19<BR>\n" );
document.write( "add 2/3 to get A6 = 19 and 2/3.<BR>\n" );
document.write( "add 2/3 to get A7 = 20 and 1/3.<BR>\n" );
document.write( "add 2/3 to get A8 = 21.\r<BR>\n" );
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document.write( "everything checks out ok so the solution looks good.\r<BR>\n" );
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