document.write( "Question 277454: the sum of the first six terms of a geometric progression is nine time the sum of the first three terms, where neither the first nor the common ratio is equal to zero. find the common ratio. \n" ); document.write( "

Algebra.Com's Answer #201986 by Edwin McCravy(20056) $\"\"$ $\"About$

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the sum of the first six terms of a geometric progression is nine time the sum of the first three terms, where neither the first nor the common ratio is equal to zero. find the common ratio.
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document.write( "Let the first term be  and the common ratio be \r\n" );
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document.write( "Sum of first three terms = \r\n" );
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document.write( "Let this sum of the first three terms be \r\n" );
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document.write( "Sum of first six terms = \r\n" );
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document.write( "Sum of first six terms = \r\n" );
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document.write( "We are given that .  Divide through by X and we have\r\n" );
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document.write( "Check: Suppose the first term is a. Then the first six terms are\r\n" );
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document.write( "a,2a,4a,8a,16a,32a\r\n" );
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document.write( "The sum of the first three terms is a+2a+4a = 7a\r\n" );
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document.write( "The sum of the first 6 terms is a+2a+4a+8a+16a+32a=63a which is 9 times 7a.\r\n" );
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document.write( "So the answer is r=2.\r\n" );
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document.write( "Edwin

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