document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119562>Question 1119562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, could you help me with this question here please?\r<BR>\n" );
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document.write( "\"Write the explicit rule for this arithmetic sequence. The 4th term = 5, and the 10th term = 23\"\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735120 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=735120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for an arithmetic sequence is:\r<BR>\n" );
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document.write( "An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "your 4th term is equal to 5 and your 10th term is equal to 23.\r<BR>\n" );
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document.write( "using the formula, you get:\r<BR>\n" );
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document.write( "A4 = A1 + (4-1) * d\r<BR>\n" );
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document.write( "A10 = A1 + (9-1) * d\r<BR>\n" );
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document.write( "these simplify to:\r<BR>\n" );
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document.write( "A4 = A1 + 3d<BR>\n" );
document.write( "A10 = A1 + 9d\r<BR>\n" );
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document.write( "you are given that A4 = 5 and A10 = 23.\r<BR>\n" );
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document.write( "the formulas become:\r<BR>\n" );
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document.write( "5 = A1 + 3d<BR>\n" );
document.write( "23 = A1 + 9d\r<BR>\n" );
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document.write( "subtract the first formula from the second to get:\r<BR>\n" );
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document.write( "18 = 6d\r<BR>\n" );
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document.write( "solve for d to get d = 3.\r<BR>\n" );
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document.write( "in both equations, replace d with 3 to get:\r<BR>\n" );
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document.write( "5 = A1 + 3 * 3<BR>\n" );
document.write( "23 = A1 + 9 * 3\r<BR>\n" );
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document.write( "these simplify to:\r<BR>\n" );
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document.write( "5 = A1 + 9<BR>\n" );
document.write( "23 = A1 + 27\r<BR>\n" );
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document.write( "solve for A1 in both equations to get:\r<BR>\n" );
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document.write( "A1 = -4 in the first equation.<BR>\n" );
document.write( "A1 = -4 in the second equation.\r<BR>\n" );
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document.write( "that's good, since A1 needed to be the same in both equations.\r<BR>\n" );
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document.write( "since A1 = -4 and d = 3, your sequence is as follows:\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "term number      term value\r\n" );
document.write( "1                  -4\r\n" );
document.write( "2                  -1\r\n" );
document.write( "3                   2\r\n" );
document.write( "4                   5 ***** 4th term in sequence.\r\n" );
document.write( "5                   8\r\n" );
document.write( "6                  11\r\n" );
document.write( "7                  14\r\n" );
document.write( "8                  17 \r\n" );
document.write( "9                  20\r\n" );
document.write( "10                 23 ***** 10th term in sequence.\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "here's a reference on arithmetic sequences.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html\" target = \"\" target = \"_blank\">https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html</a>\r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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