document.write( "Question 388661: Two terms of an arithmetic sequence are a7 = 33 and a22 = 138. Find a rule for the nth term. \n" ); document.write( "
Algebra.Com's Answer #275022 by Edwin McCravy(20056)\"\" \"About 
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document.write( "\"a%5B7%5D+=+33\" and \"a%5B22%5D+=+138\"\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "Substitute n=7\r\n" );
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document.write( "\"a%5B7%5D=a%5B1%5D%2B%287-1%29d\"\r\n" );
document.write( "\"a%5B7%5D=a%5B1%5D%2B6d\"\r\n" );
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document.write( "Substitute 33 for \"a%5B7%5D\"\r\n" );
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document.write( "\"33=a%5B1%5D%2B6d\"\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "Substitute n=22\r\n" );
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document.write( "\"a%5B22%5D=a%5B1%5D%2B%2822-1%29d\"\r\n" );
document.write( "\"a%5B22%5D=a%5B1%5D%2B21d\"\r\n" );
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document.write( "Substitute 138 for \"a%5B22%5D\"\r\n" );
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document.write( "\"138=a%5B1%5D%2B21d\"\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "\"system%2833=a%5B1%5D%2B6d%2C+138=a%5B1%5D%2B21d%29\"\r\n" );
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document.write( "Solve that by substitution and get \"a%5B1%5D=-9\" and \"d=7\"\r\n" );
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document.write( "So the rule is\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "\"a%5Bn%5D=-9%2B%28n-1%297\"\r\n" );
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document.write( "\"a%5Bn%5D=-9%2B7%28n-1%29\"\r\n" );
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document.write( "\"a%5Bn%5D=-9%2B7n-7\"\r\n" );
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document.write( "\"a%5Bn%5D=7n-16\"\r\n" );
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document.write( "To check substitute n = 7 and n = 22 and see if we get 33 and 138\r\n" );
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document.write( "\"a%5B7%5D=7%287%29-16\"\r\n" );
document.write( "\"a%5B7%5D=49-16\"\r\n" );
document.write( "\"a%5B7%5D=33\"\r\n" );
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document.write( "\"a%5B22%5D=7%2822%29-16\"\r\n" );
document.write( "\"a%5B7%5D=154-16\"\r\n" );
document.write( "\"a%5B7%5D=138\"\r\n" );
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document.write( "It checks, so the answer is\r\n" );
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document.write( "\"a%5Bn%5D=7n-16\"\r\n" );
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document.write( "Edwin

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