document.write( "Question 1012940: find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108 251. \n" ); document.write( "

Algebra.Com's Answer #629076 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108 251.
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document.write( "This progression is geometric with the first term 11 and the common ratio of 3.\r\n" );
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document.write( "Use the formula for the sum of the first n terms of a geometric progression:\r\n" );
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document.write( " = . \r\n" );
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document.write( "(see the lesson Geometric progressions in this site).\r\n" );
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document.write( "Substitute here a = 11 and q = 3. You will get an equation\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " =  = 9841,\r\n" );
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document.write( " = 2*9841 + 1 = 19683 = 3^9.\r\n" );
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document.write( "Hence, n = 9.\r\n" );
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document.write( "Answer. n = 9.\r\n" );
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