document.write( "Question 1202440: Calculate the sum of the series 4 + 12 + 36 + ... + 2916.\r
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Algebra.Com's Answer #837282 by ikleyn(52794)\"\" \"About 
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document.write( "The sequense  4, 12, 36, . . ., 2916  is a geometric progression\r\n" );
document.write( "with the first term  a= 4  and the common ratio of r= 3  \r\n" );
document.write( "(sinse 12/4 = 3 and the ratio of each next term to the current term is 3).\r\n" );
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document.write( "Find the number of term. Use the formula for the n-th term\r\n" );
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document.write( "    2916 = \"4%2A3%5E%28n-1%29\".\r\n" );
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document.write( "It gives  2916/4 = 729 = \"3%5E%28n-1%29\".  But 729 = \"7%5E6\";  therefore, n-1 = 7 and n= 7.\r\n" );
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document.write( "CHECK.  \"4%2A3%5E%287-1%29\" = use your calculator = 2916,  correct.\r\n" );
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document.write( "To find the sum of this GP, use the general formula for the sum of a GP\r\n" );
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document.write( "    \"S%5Bn%5D\" = \"a%2A%28%28r%5En-1%29%2F%28r-1%29%29\".\r\n" );
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document.write( "It gives at n= 7\r\n" );
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document.write( "    \"S%5B7%5D\" = \"4%2A%28%283%5E7-1%29%2F%283-1%29%29\" = \"%284%2F2%29%2A%283%5E7-1%29\" = \"2%2A%283%5E7-1%29\" = use your calculator = 4372.   ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On geometric progressions,  see introductory lessons\r
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\n" ); document.write( "\n" ); document.write( "Now you see from my post  (I hope),  how much is it better
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