document.write( "Question 612425: write a rule for the nth term of the arithmetic sequence
\n" ); document.write( "1. a11=29; a20=101
\n" ); document.write( "2.a6=-31; a14=-135 \n" ); document.write( "
Algebra.Com's Answer #385557 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The formula to learn for the nth term of arithmetic\r\n" );
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document.write( "an = a1 + (n-1)·d\r\n" );
document.write( "I'll work the second one.  But I'll just give you the answer \r\n" );
document.write( "to the first one, so you'll have to do it by yourself, but \r\n" );
document.write( "you do it exactly like the second one. \r\n" );
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document.write( "The answer to the first one is\r\n" );
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document.write( "an = 8n - 59 \r\n" );
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document.write( "---------------------\r\n" );
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document.write( "2. a6=-31; a14=-135\r\n" );
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document.write( "an = a1 + (n-1)·d\r\n" );
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document.write( "Substitute n=6\r\n" );
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document.write( "a6 = a1 + (6-1)d\r\n" );
document.write( "-31 = a1 + 5d\r\n" );
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document.write( "Substitute n=14\r\n" );
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document.write( "a14 = a1 + (14-1)d\r\n" );
document.write( "-135 = a1 + (13)d\r\n" );
document.write( "-135 = a1 + 13d\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( "-135 = a1 + 13d\r\n" );
document.write( " -31 = a1 +  5d\r\n" );
document.write( "Multiply the second equation through by -1\r\n" );
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document.write( "-135 =  a1 + 13d\r\n" );
document.write( "  31 = -a1 -  5d\r\n" );
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document.write( "Add those two equations:\r\n" );
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document.write( "-135 =  a1 + 13d\r\n" );
document.write( "  31 = -a1 -  5d\r\n" );
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document.write( "-104 =       8d\r\n" );
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document.write( "\"%28-104%29%2F8\" = d\r\n" );
document.write( "\"-13\" = d\r\n" );
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document.write( "Substituting that in\r\n" );
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document.write( " -31 = a1 + 5d\r\n" );
document.write( " -31 = a1 + 5(-13)\r\n" );
document.write( " -31 = a1 - 65\r\n" );
document.write( "  34 = a1 \r\n" );
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document.write( "So \r\n" );
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document.write( "an = a1 + (n-1)·d\r\n" );
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document.write( "becomes\r\n" );
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document.write( "an = 34 + (n-1)·(-13)\r\n" );
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document.write( "an = 34 - 13(n-1)\r\n" );
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document.write( "an = 34 - 13n + 13\r\n" );
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document.write( "an = 47 - 13n\r\n" );
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document.write( "Edwin

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