document.write( "Question 1090952: When a group of 50 consecutive multiples of 7 is added
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Algebra.Com's Answer #705394 by Edwin McCravy(20067)\"\" \"About 
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When a group of 50 consecutive multiples of 7 is added
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document.write( "Let k the smallest integer such that 7k is the smallest multiple\r\n" );
document.write( "of 7 such that the sum of the series\r\n" );
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document.write( "7k+(7k+7)+(7k+14)+ ∙∙∙ (to 50 terms) = 12075\r\n" );
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document.write( "Th formula for the sum of an arithmetic series is\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22%2Ad%29\", where n=50, a1=7k, d=7\r\n" );
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document.write( "\"S%5B50%5D=expr%2850%2F2%29%282%287k%29%2B%2850-1%29%5E%22%22%2A7%29\"\r\n" );
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document.write( "\"S%5B50%5D=%2825%29%2814k%2B49%2A7%29\"\r\n" );
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document.write( "\"S%5B50%5D=%2825%29%2814k%2B343%29\"\r\n" );
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document.write( "And since S50=12075\r\n" );
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document.write( "\"%2825%29%2814k%2B343%29=12075\"\r\n" );
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document.write( "Divide both sides by 25\r\n" );
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document.write( "\"14k%2B343=483\"\r\n" );
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document.write( "\"14k=140\"\r\n" );
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document.write( "\"k=10\" \r\n" );
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document.write( "The smallest integer = 7k = 7(10) = 70\r\n" );
document.write( "The largest integer is the 50th term\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad\"\r\n" );
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document.write( "\"a%5B50%5D=70%2B%2850-1%29%2A7\"\r\n" );
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document.write( "\"a%5B50%5D=70%2B49%2A7\"\r\n" );
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document.write( "\"a%5B50%5D=70%2B343\"\r\n" );
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document.write( "\"a%5B50%5D=413\"\r\n" );
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document.write( "Answers: smallest = 70, biggest = 413\r\n" );
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document.write( "Edwin
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