document.write( "Question 412077: Hello, can somebody please help me with this question I don't understand it\r
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Algebra.Com's Answer #289505 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Hello, can somebody please help me with this question I don't understand it\r
\n" ); document.write( "\n" ); document.write( "The 8th term of an arithmetic sequence is 25 and the 20th term is -11. Find the first term of the sequence and the common difference and use those to write the general term.\r
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document.write( "The other tutor's answer is wrong.\r\n" );
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document.write( "__, __, __, __, __, __, __, 25, __, __, __, __, __, __, __, __, __, __, __, -11, __, ...   \r\n" );
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document.write( "The general term of any arithmetic sequence is the formula\r\n" );
document.write( "for the nth term which is\r\n" );
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document.write( "an = a1 + (n - 1)d\r\n" );
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document.write( "Substitute 8 for n:\r\n" );
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document.write( "a8 = a1 + (8 - 1)d\r\n" );
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document.write( "a8 = a1 + 7d\r\n" );
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document.write( "Substitute 25 for a8\r\n" );
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document.write( "25 = a1 + 7d\r\n" );
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document.write( "a1 + 7d = 25\r\n" );
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document.write( "an = a1 + (n - 1)d\r\n" );
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document.write( "Substitute 20 for n:\r\n" );
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document.write( "a20 = a1 + (20 - 1)d\r\n" );
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document.write( "a20 = a1 + 19d\r\n" );
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document.write( "Substitute -11 for a20\r\n" );
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document.write( "-11 = a1 + 19d\r\n" );
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document.write( "a1 + 19d = -11\r\n" );
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document.write( "Now we have the system of equations:\r\n" );
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document.write( "a1 +  7d =  25\r\n" );
document.write( "a1 + 19d = -11\r\n" );
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document.write( "Solve the first one for a1\r\n" );
document.write( "      a1 =  25 - 7d\r\n" );
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document.write( "Substitute (25 - 7d) for a1\r\n" );
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document.write( "(25 - 7d) + 19d = -11\r\n" );
document.write( "  25 - 7d + 19d = -11\r\n" );
document.write( "       25 + 12d = -11\r\n" );
document.write( "            12d = -36\r\n" );
document.write( "              d = -3\r\n" );
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document.write( "             a1 =  25 - 7d\r\n" );
document.write( "             a1 =  25 - 7(-3)\r\n" );
document.write( "             a1 =  25 + 21\r\n" );
document.write( "             a1 =  46\r\n" );
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document.write( "So a1 = 46 is the first term of the sequence and d = -3 is the common\r\n" );
document.write( "difference.   \r\n" );
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document.write( "So the arithmetic sequence is:\r\n" );
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document.write( "46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, -2, -5, -8, -11, -14, ...\r\n" );
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document.write( "The general term is found by substituting a1 = 46 and d = -3 in the\r\n" );
document.write( "formula for the nth term:\r\n" );
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document.write( "an = a1 + (n - 1)d\r\n" );
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document.write( "an = 46 + (n - 1)(-3)\r\n" );
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document.write( "an = 46 - 3(n - 1)\r\n" );
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document.write( "an = 46 - 3n + 3\r\n" );
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document.write( "an = 49 - 3n\r\n" );
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document.write( "That's the general term.\r\n" );
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document.write( "Edwin
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