document.write( "Question 738254: 1,2,0.5,5,0.25,8..... Calculate the sum of 100 terms of the sequence \n" ); document.write( "
Algebra.Com's Answer #450970 by Edwin McCravy(20056)\"\" \"About 
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document.write( "1,2,0.5,5,0.25,8..... \r\n" );
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document.write( "Change the decimals to fractions:\r\n" );
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document.write( "1,  2, \"1%2F2\", 5, \"1%2F4\", 8, ...\r\n" );
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document.write( "the odd numbered terms are 50 terms of this geometric sequence\r\n" );
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document.write( "1, \"1%2F2\", \"1%2F4\", ...\r\n" );
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document.write( "We use the formula \r\n" );
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document.write( "Sn = \"a%5B1%5D%281-r%5En%29%2F%281-r%29\" \r\n" );
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document.write( "where n=50, a1 = 1, r = \"1%2F2\"\r\n" );
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document.write( "S50 = \"1%281-%281%2F2%29%5E50%29%2F%281-1%2F2%29\" \r\n" );
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document.write( "Since \"%281%2F2%29%5E50\" is so small it is negligible and\r\n" );
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document.write( "that is essentially \"1%2F%281%2F2%29\" = 2\r\n" );
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document.write( "the even numbered terms are 50 terms of this arithmetic sequence\r\n" );
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document.write( "2,5,8,...\r\n" );
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document.write( "We use the formula\r\n" );
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d]\r\n" );
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document.write( "S50 = \"50%2F2\"[2·2 + (50-1)3]\r\n" );
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document.write( "S50 = 25[4 + 49·3]\r\n" );
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document.write( "S50 = 3775\r\n" );
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document.write( "Answer:  2 + 3775 = 3777. \r\n" );
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document.write( "Edwin
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