document.write( "Question 974719: determine whether each sequence is arithmetic or geometric, find the explicit rule write it in summation notation, and calculate the sum
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Algebra.Com's Answer #596730 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "A sequence in arithmetic if any two pairs of succesive terms have the same common difference.\r\n" );
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document.write( "A sequence in geometric if any two pairs of succesive terms have the same common quotient (or ratio).\r\n" );
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document.write( "A) is geometric because 1÷(1/4) = 1×(4/1) = 4 and 4÷1 = 4 = common ratio = r\r\n" );
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document.write( "The formula for the nth term of a geometric sequence is:\r\n" );
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document.write( "\"a%5Bn%5D\"\"%22%22=%22%22\"\"a%5B1%5Dr%5E%28n-1%29\" where \"a%5B1%5D\" is the first term\r\n" );
document.write( "and r is the common ratio:\r\n" );
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document.write( "\"a%5Bn%5D\"\"%22%22=%22%22\"\"expr%281%2F4%29%2A%284%29%5E%28n-1%29\"\"%22%22=%22%22\"\"4%5E%28-1%29%2A4%5E%28n-1%29\"\"%22%22=%22%22\"\"4%5E%28-1%2Bn-1%29\"\"%22%22=%22%22\"\"4%5E%28n-2%29\"\r\n" );
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document.write( "So \"a%5Bn%5D\"\"%22%22=%22%22\"\"4%5E%28n-2%29\"\r\n" );
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document.write( "B) is arithmetic because 7-2 = 5 and 12-7 = 5 = common difference = d\r\n" );
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document.write( "The formula for the nth term of an arithmetic sequence is:\r\n" );
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document.write( "\"a%5Bn%5D\"\"%22%22=%22%22\"\"a%5B1%5D%2B%28n-1%29d\" where \"a%5B1%5D\" is the first term\r\n" );
document.write( "and d is the common ratio:\r\n" );
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document.write( "\"a%5Bn%5D\"\"%22%22=%22%22\"\"2%2B%28n-1%29%285%29\"\"%22%22=%22%22\"\"2%2B5%28n-1%29\"\"%22%22=%22%22\"\"2%2B5n-5\"\"%22%22=%22%22\"\"5n-3\"\r\n" );
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document.write( "So \"a%5Bn%5D\"\"%22%22=%22%22\"\"5n-3\"\r\n" );
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document.write( "Edwin
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