document.write( "Question 949553: WHAT IS THE 30TH TERM OF GEOMETRIC SEQUENCE IF THE 10TH IS 3/512 AND 15TH IS 3/16384 \n" ); document.write( "
Algebra.Com's Answer #579744 by Edwin McCravy(20056)\"\" \"About 
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WHAT IS THE 30TH TERM OF GEOMETRIC SEQUENCE IF THE 10TH IS 3/512 AND 15TH IS 3/16384
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document.write( "Use \r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\"\r\n" );
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document.write( "Substitute \"n=10\", \"a%5B10%5D=3%2F512=3%2F2%5E9\"\r\n" );
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document.write( "\"a%5B10%5D=a%5B1%5Dr%5E%2810-1%29\"\r\n" );
document.write( "\"3%2F2%5E9=a%5B1%5Dr%5E9\"\r\n" );
document.write( "Divide both sides by \"r%5E9\"\r\n" );
document.write( "\"3%2F%282%5E9r%5E9%29=a%5B1%5D\"\r\n" );
document.write( "\"3%2F%282r%29%5E9=a%5B1%5D\"\r\n" );
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document.write( "Substitute \"n=15\", \"a%5B15%5D=3%2F16384=+3%2F2%5E14\"\r\n" );
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document.write( "\"a%5B15%5D=a%5B1%5Dr%5E%2815-1%29\"\r\n" );
document.write( "\"3%2F2%5E14=a%5B1%5Dr%5E14\"\r\n" );
document.write( "Divide both sides by \"r%5E14\"\r\n" );
document.write( "\"3%2F%282%5E14r%5E14%29=a%5B1%5D\"\r\n" );
document.write( "\"3%2F%282r%29%5E14=a%5B1%5D\"\r\n" );
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document.write( "Equate the two expressions for \"a%5B1%5D\"\r\n" );
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document.write( "\"3%2F%282r%29%5E9=3%2F%282r%29%5E14\"\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "\"1%2F%282r%29%5E9=1%2F%282r%29%5E14\"\r\n" );
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document.write( "Cross-multiply\r\n" );
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document.write( "\"%282r%29%5E14+=+%282r%29%5E9\"\r\n" );
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document.write( "Divide both sides by \"%282r%29%5E9\"\r\n" );
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document.write( "\"%282r%29%5E5+=+1\"\r\n" );
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document.write( "Take 5th roots of both sides\r\n" );
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document.write( "\"2r=1\"\r\n" );
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document.write( "\"r=1%2F2\"\r\n" );
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document.write( "Substitute 2r=1 in\r\n" );
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document.write( "\"3%2F%282r%29%5E9=a%5B1%5D\"\r\n" );
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document.write( "\"3%2F%281%29%5E9=a%5B1%5D\"\r\n" );
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document.write( "\"3%2F1=a%5B1%5D\"\r\n" );
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document.write( "\"3=a%5B1%5D\"\r\n" );
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document.write( "Now you finish by substituting n=30, a1=3, and \"r=1%2F2\"\r\n" );
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document.write( "into\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\"\r\n" );
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document.write( "To find a30.\r\n" );
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document.write( "Edwin
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