document.write( "Question 695853: Which term of the sequence 20, 77/4,37/2,71/4.........is first negative term? \n" ); document.write( "
Algebra.Com's Answer #430043 by Edwin McCravy(20056)\"\" \"About 
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document.write( "20, \"77%2F4\", \"37%2F2\", \"71%2F4\"\r\n" );
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document.write( "2nd term - 1st term = \"77%2F4\" - 20 = \"77%2F4\" - \"80%2F4\" = \"-3%2F4\".\r\n" );
document.write( "3rd term - 2nd term = \"37%2F2\" - \"77%2F4\" = \"74%2F4\" - \"77%2F4\" = \"-3%2F4\".\r\n" );
document.write( "4th term - 3rd term = \"71%2F4\" - \"37%2F2\" = \"71%2F4\" - \"74%2F4\" = \"-3%2F4\".\r\n" );
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document.write( "So the common difference is d = \"-3%2F4\"\r\n" );
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document.write( "Use the nth term formula for an arithmetic sequence.\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "1st term = a1 = 20, d = \"-3%2F4\"\r\n" );
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document.write( "an = 20 + (n-1)\"%28-3%2F4%29\"\r\n" );
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document.write( "We set that < 0 to make it negative, and solve for n:\r\n" );
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document.write( "20 + (n-1)\"%28-3%2F4%29\" < 0\r\n" );
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document.write( "Multiply both sides by 4\r\n" );
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document.write( "80 + (n-1)(-3) < 0\r\n" );
document.write( "80 + (-3)(n-1) < 0\r\n" );
document.write( "   80 - 3(n-1) < 0\r\n" );
document.write( "   80 - 3n + 3 < 0\r\n" );
document.write( "       83 - 3n < 0\r\n" );
document.write( "           -3n < -83\r\n" );
document.write( "             n > \"27%262%2F3\"\r\n" );
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document.write( "So the 28th term is the first negative term.\r\n" );
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document.write( "That term is:\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "a28 = 20 + (28-1)\"%28-3%2F4%29\"\r\n" );
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document.write( "a28 = 20 + (27)\"%28-3%2F4%29\"\r\n" );
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document.write( "a28 = 20 + \"%28-81%2F4%29\"\r\n" );
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document.write( "a28 = \"80%2F4\" - \"81%2F4\"\r\n" );
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document.write( "a28 = \"-1%2F4\"\r\n" );
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document.write( "Edwin
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