document.write( "Question 898542: In a geometric series, the sum of the first three terms is 304, and the sum of the first six terms is 1330. Find the sum of the first seven terms. \n" ); document.write( "
Algebra.Com's Answer #544886 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
In a geometric series, the sum of the first three terms is 304,
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document.write( "\"a%5B1%5D%2Ba%5B1%5Dr%2Ba%5B1%5Dr%5E2\"\"%22%22=%22%22\"\"304\"\r\n" );
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document.write( "(1)   \"a%5B1%5D%281%2Br%2Br%5E2%29\"\"%22%22=%22%22\"\"304\"\r\n" );
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\n" ); document.write( "and the sum of the first six terms is 1330.
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document.write( "So the sum of the 3rd, 4th and 5th terms only is 1330-304 = 1026\r\n" );
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document.write( "\"a%5B1%5Dr%5E3%2Ba%5B1%5Dr%5E4%2Ba%5B1%5Dr%5E5\"\"%22%22=%22%22\"\"1026\"\r\n" );
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document.write( "(2)   \"a%5B1%5Dr%5E3%281%2Br%2Br%5E2%29\"\"%22%22=%22%22\"\"1026\"\r\n" );
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document.write( "Dividing equals by equals, equation (2) by equation (1)\r\n" );
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document.write( "    \"%28a%5B1%5Dr%5E3%281%2Br%2Br%5E2%29%29%2F%28a%5B1%5D%281%2Br%2Br%5E2%29%29\"\"%22%22=%22%22\"\"1026%2F304\"\r\n" );
document.write( "\r\n" );
document.write( "    \"%22%22=%22%22\"\"27%2F8\"\r\n" );
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document.write( "    \"r%5E3\"\"%22%22=%22%22\"\"27%2F8\"\r\n" );
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document.write( "Taking cube roots of both sides\r\n" );
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document.write( "    \"r\"\"%22%22=%22%22\"\"3%2F2\"\r\n" );
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document.write( "Substitute in equation (1)\r\n" );
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document.write( "(1)   \"a%5B1%5D%281%2Br%2Br%5E2%29\"\"%22%22=%22%22\"\"304\"\r\n" );
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document.write( "      \"a%5B1%5D%281%2B3%2F2%2B%283%2F2%29%5E2%29\"\"%22%22=%22%22\"\"304\"\r\n" );
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document.write( "      \"a%5B1%5D%281%2B3%2F2%2B9%2F4%29\"\"%22%22=%22%22\"\"304\"\r\n" );
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document.write( "Multiply the terms in the parentheses and the right side by 4\r\n" );
document.write( "to clear of fractions:\r\n" );
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document.write( "      \"a%5B1%5D%284%2B6%2B9%29\"\"%22%22=%22%22\"\"1216\"\r\n" );
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document.write( "      \"a%5B1%5D%2819%29\"\"%22%22=%22%22\"\"1216\"\r\n" );
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document.write( "Divide both sides by 19\r\n" );
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document.write( "      \"a%5B1%5D\"\"%22%22=%22%22\"\"1216%2F19\"\r\n" );
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document.write( "      \"a%5B1%5D\"\"%22%22=%22%22\"\"64\"\r\n" );
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\n" ); document.write( "Find the sum of the first seven terms.
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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\"\r\n" );
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document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"%2864%28%283%2F2%29%5E7-1%29%29%2F%283%2F2-1%29\"\r\n" );
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document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"%2864%282187%2F128-1%29%29%2F%283%2F2-1%29\"\r\n" );
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document.write( "Multiply the top out, the 16 goes into the 128 2 times,\r\n" );
document.write( "and write the 1 on the bottom as \"2%2F2\"\r\n" );
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document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"%282187%2F2-64%29%2F%283%2F2-2%2F2%29\"\r\n" );
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document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"%282187%2F2-64%29%2F%281%2F2%29\"\r\n" );
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document.write( "Multiply top and bottom by 2\r\n" );
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document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"2%282187%2F2-64%29%2F%282%2Aexpr%281%2F2%29%29\"\r\n" );
document.write( " \r\n" );
document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"%282187-128%29%2F1\"\r\n" );
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document.write( "\"S%5B7%5D\"\"%22%22=%22%22\"\"2059\"\r\n" );
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document.write( "Edwin
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