document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085451>Question 1085451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The 18th and 52nd terms of an arithmetic sequence are 3and 173, respectively. Which term is 38? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699531 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=699531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if it's an arithmetic sequence, then there is a common difference between terms.\r<BR>\n" );
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document.write( "your 18th term is equal to 3 and your 52d term is equal to 173.\r<BR>\n" );
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document.write( "take 52 and subtract 18 to get 34\r<BR>\n" );
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document.write( "take 173 and subtract 3 to get 170\r<BR>\n" );
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document.write( "170 / 34 = 5\r<BR>\n" );
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document.write( "the common difference difference between one element and the next element is 5.\r<BR>\n" );
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document.write( "in order to go from 3 to 38, you have to add 35\r<BR>\n" );
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document.write( "35 / 5 is equal to 7\r<BR>\n" );
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document.write( "3 is the 18th term.\r<BR>\n" );
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document.write( "add 7 to that and you get 35 is the 18 + 7 = 25th term.\r<BR>\n" );
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document.write( "how do we know this is good?\r<BR>\n" );
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document.write( "you can create your sequence starting from 3 and working upwards 5 at a time, or, if you know the formula for an arithmetic sequence, you can use that.\r<BR>\n" );
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document.write( "the formula for an arithmetic sequence is An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "An is the nth term.<BR>\n" );
document.write( "A1 is the first term<BR>\n" );
document.write( "n is then umber of terms<BR>\n" );
document.write( "d is the common difference between terms.\r<BR>\n" );
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document.write( "you just solved for the common difference and you know at least one of the nth terms.\r<BR>\n" );
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document.write( "we'll take term  number 18.\r<BR>\n" );
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document.write( "the formula of An = A1 + (n-1) * d becomes:\r<BR>\n" );
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document.write( "3 = A1 + (17 * 5)\r<BR>\n" );
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document.write( "solve for A1 to get A1 = 3 - (17 * 5) which becomes A1 = 3 - 85 which becomes A1 = -82\r<BR>\n" );
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document.write( "we now have A1 = -82 and d = 5\r<BR>\n" );
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document.write( "A18 = -82 + 17 * 5 = 3\r<BR>\n" );
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document.write( "A52 = -82 + 51 * 5 = 173\r<BR>\n" );
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document.write( "A25 = -82 + 24 * 5 = 38\r<BR>\n" );
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document.write( "everything checks out so we're good.\r<BR>\n" );
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document.write( "you didn't need the formula to solve this.<BR>\n" );
document.write( "you just had to know that it was an arithmetic sequence which means there's a common difference between each element in the sequence.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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