document.write( "Question 324238: First time with college algebra, what is \"a%5Bn%5D\" formula to help me remember
\n" ); document.write( "about sequences of numbers. \n" ); document.write( "
Algebra.Com's Answer #232069 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If it's an arithmetic sequence like\r\n" );
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document.write( "3, 7, 11, 15, ...\r\n" );
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document.write( "Then the first term, 3, is called \"a%5B1%5D\", the second term, 7, is called \r\n" );
document.write( "\"a%5B2%5D\", etc.  The common difference is the amount that's added to each\r\n" );
document.write( "number to get the next one. To get from 3 to 7 you add 4. To get from 7 to 11\r\n" );
document.write( "you add 4, to get from 11 to 15 you add 4.  So 4 is the common difference d\r\n" );
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document.write( "The get the equation for the nth term, you use the formula\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "\"a%5Bn%5D=3%2B%28n-1%29%2A4\"\r\n" );
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document.write( "\"a%5Bn%5D=3%2B4%28n-1%29\"\r\n" );
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document.write( "\"a%5Bn%5D=3%2B4n-4\"\r\n" );
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document.write( "\"a%5Bn%5D=4n-1\"\r\n" );
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document.write( "and to get the sum of the first n terms \"S%5Bn%5D\":\r\n" );
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document.write( "\"S%5Bn%5D=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\"\r\n" );
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document.write( "\"S%5Bn%5D=%28n%2F2%29%283%2B%284n-1%29%29\"\r\n" );
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document.write( "\"S%5Bn%5D=%28n%2F2%29%282%2B4n%29\"\r\n" );
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document.write( "\"S%5Bn%5D=%28n%2F2%292%281%2B2n%29\"\r\n" );
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document.write( "\"S%5Bn%5D=n%281%2B2n%29\"\r\n" );
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document.write( "f it's a geometric sequence like\r\n" );
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document.write( "4, 12, 36, 108, ...\r\n" );
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document.write( "Then the first term, 3, is called \"a%5B1%5D\", the second term, 12, is called \r\n" );
document.write( "\"a%5B2%5D\", etc.  The common ratio is the amount that each number is\r\n" );
document.write( "multiplied by to get the next one. To get from 4 to 12 you multiply by 3. To \r\n" );
document.write( "get from 12 to 36 you multiply by 3, to get from 36 to 108 you multiply by 3.  \r\n" );
document.write( "So 3 is the common ratio r.\r\n" );
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document.write( "The get the equation for the nth term, you use the formula\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"\r\n" );
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document.write( "\"a%5Bn%5D=4%2A3%5E%28n-1%29\"\r\n" );
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document.write( "and to get the sum of the first n terms \"S%5Bn%5D\":\r\n" );
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document.write( "\"S%5Bn%5D=%28a%5B1%5D%28r%5En-1%29%29%2F%28r-1%29\"\r\n" );
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document.write( "\"S%5Bn%5D=%284%283%5En-1%29%29%2F%283-1%29\"\r\n" );
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document.write( "\"S%5Bn%5D=%284%283%5En-1%29%29%2F2\"\r\n" );
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document.write( "\"S%5Bn%5D=2%283%5En-1%29\"\r\n" );
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document.write( "Edwin
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