document.write( "Question 959558: Can you find the sum of the first 60 terms in the series 2+6+4+12+6+24 \n" ); document.write( "
Algebra.Com's Answer #586577 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Break the 60 term series up into the sum of the 30 term \r\n" );
document.write( "series of odd numbered terms and the 30 term series of the\r\n" );
document.write( "even numbered terms.  That is\r\n" );
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document.write( "2+6+4+12+6+24+... = 2+4+6+... +6+12+24+... \r\n" );
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document.write( "The first series is arithmetic and the second one is geometric:\r\n" );
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document.write( "to find the sum of 2+4+6+... to 30 terms we use the formula:\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%282a%5E%22%22%2B%28n-1%29d%29\", where \"a%5B1%5D=2\", \"n=30\", and \"d=2\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"expr%2830%2F2%29%282%282%29%5E%22%22%2B%2830-1%292%29\" \r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"15%284%5E%22%22%2B%2829%292%29\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"15%284%2B58%29\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"15%2862%29\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"930\"\r\n" );
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document.write( "---\r\n" );
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document.write( "To find the sum of 6+12+24+... to 30 terms we use the formula:\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"%28a%5B1%5D%28r%5En-1%29%29%2F%28r-1%29\", where \"a%5B1%5D=6\", \"n=30\", and \"r=2\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"6%282%5E30-1%29%2F%282-1%29\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"6%281073741824-1%29%2F%281%29\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"6%281073741823%29\"\r\n" );
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document.write( "\"S%5B30%5D\"\"%22%22=%22%22\"\"6442450938\"\r\n" );
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document.write( "----------------\r\n" );
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document.write( "The sum of the two sequences is  930+6442450938 = 6442451868\r\n" );
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document.write( "Edwin
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