document.write( "Question 830892: the 3rd and 6th term of a geometric progression are 48 and 14 2/9 respectively. Write down the 1st 4 terms of the geometric progression. \n" ); document.write( "
Algebra.Com's Answer #501010 by Edwin McCravy(20056)\"\" \"About 
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the 3rd and 6th term of a geometric progression are 48 and 14 2/9 respectively.
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document.write( "a1, a2, a3=48, a4, a5, a6=\"14%262%2F9\"\r\n" );
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document.write( "You need this formula for the nth term:\r\n" );
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document.write( "an = a1·r(n-1)\r\n" );
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document.write( "[Some books and teachers use \"t\" for \"term\" instead of \"a\".\r\n" );
document.write( "I'll use \"a\".]\r\n" );
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\n" ); document.write( "the 3rd and 6th term of a geometric progression are 48 and 14 2/9 respectively.
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document.write( "a3 = a1·r(3-1)\r\n" );
document.write( "48 = a1·r2\r\n" );
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document.write( "a6 = a1·r(6-1)\r\n" );
document.write( "\"14%262%2F9\" = a1·r5\r\n" );
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document.write( "Change \"14%262%2F9\" to an improper fraction \"128%2F9\"\r\n" );
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document.write( "\"128%2F9\" = a1·r5\r\n" );
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document.write( "Clear of fractions by multipolying both sides by 9\r\n" );
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document.write( "128 = 9a1·r5\r\n" );
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document.write( "So you have this system of equations:\r\n" );
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document.write( " 48 = a1·r2\r\n" );
document.write( "128 = 9a1·r5\r\n" );
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document.write( "Solve the first for a1\r\n" );
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document.write( "\"48%2Fr%5E2\"\"%22%22=%22%22\"\"%28a%5B1%5Dr%5E2%29%2Fr%5E2\"\r\n" );
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document.write( "\"48%2Fr%5E2\"\"%22%22=%22%22\"\"%28a%5B1%5Dcross%28r%5E2%29%29%2Fcross%28r%5E2%29\"\r\n" );
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document.write( "\"48%2Fr%5E2\" = a1\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "128 = 9\"%2848%2Fr%5E2%29\"·r5\r\n" );
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document.write( "128 = \"432r%5E5%2Fr%5E2\"\r\n" );
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document.write( "Divide on the right by subtracting exponents:\r\n" );
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document.write( "128 = 432r³\r\n" );
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document.write( "Divide both sides by 432\r\n" );
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document.write( "\"128%2F432\" = \"432r%5E3%2F432\"\r\n" );
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document.write( "Reduce the fraction on the left and cancel on the right:\r\n" );
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document.write( "\"8%2F27\" = \"cross%28432%29r%5E3%2Fcross%28432%29\"\r\n" );
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document.write( "\"8%2F27\" = r³\r\n" );
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document.write( "The cube root of 8 is 2 and the cube root of 27 is 3, so\r\n" );
document.write( "taking cube roots of both sides:\r\n" );
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document.write( "\"2%2F3\" = r\r\n" );
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document.write( "Substitute for r in\r\n" );
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document.write( "\"48%2Fr%5E2\" = a1\r\n" );
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document.write( "\"48%2F%282%2F3%29%5E2\" = a1\r\n" );
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document.write( "\"48%2F%28%284%2F9%29%29\" = a1 \r\n" );
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document.write( "To divide by a fraction, invert it and multiply\r\n" );
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document.write( "\"48%2A%289%2F4%29\" = a1\r\n" );
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document.write( "4 goes into 48 12 times:\r\n" );
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document.write( " 12\r\n" );
document.write( "\"cross%2848%29%2A%289%2Fcross%284%29%29\" = a1\r\n" );
document.write( "     1\r\n" );
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document.write( "108 = a1\r\n" );
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\n" ); document.write( "Write down the 1st 4 terms of the geometric progression.
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document.write( "1st term = \"108\",\r\n" );
document.write( "2nd term = \"108%2Aexpr%282%2F3%29\"\"%22%22=%22%22\"\"72\"\r\n" );
document.write( "3rd term = \"72%2Aexpr%282%2F3%29\"\"%22%22=%22%22\"\"48\"\r\n" );
document.write( "4th term = \"48%2Aexpr%282%2F3%29\"\"%22%22=%22%22\"\"32\"\r\n" );
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document.write( "the 3rd term checks, but to check the whole thing,\r\n" );
document.write( "lets see if the 6th term is \"14%262%2F9\"\r\n" );
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document.write( "5th term = \"32%2Aexpr%282%2F3%29\"\"%22%22=%22%22\"\"64%2F3\"\"%22%22=%22%22\"\"21%261%2F3\"\r\n" );
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document.write( "6th term = \"expr%2864%2F3%29%2Aexpr%282%2F3%29\"\"%22%22=%22%22\"\"128%2F9\"\"%22%22=%22%22\"\"14%262%2F9\"\r\n" );
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document.write( "So it checks.\r\n" );
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document.write( "Edwin
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