document.write( "Question 1053828: what is the formula of sequence 1,2,1,2,1,2... \n" ); document.write( "
Algebra.Com's Answer #669014 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "Observe that from halfway between 1 and 2, which is , \r\n" );
document.write( "we go down from  by  to 1, then\r\n" );
document.write( "we go up from  by  to 2, then\r\n" );
document.write( "we go down from  by  to 1, then\r\n" );
document.write( "we go up from  by  to 2, then\r\n" );
document.write( "etc., etc., etc., ...\r\n" );
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document.write( "We know that the formula  goes down and up\r\n" );
document.write( "-1,1,-1,1,-1,1,...\r\n" );
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document.write( "So we can use that as a multiplier of  to go down\r\n" );
document.write( "and up from ,\r\n" );
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document.write( "So to get the 1st term we take  and add\r\n" );
document.write( ", which is -1, times , to go down\r\n" );
document.write( "to 1.\r\n" );
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document.write( "Then to get the 2nd term we take  and add\r\n" );
document.write( ", which is +1, times , to go up\r\n" );
document.write( "to 2.\r\n" );
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document.write( "Then to get the 3rd term we take  and add\r\n" );
document.write( ", which is -1, times , to go down\r\n" );
document.write( "to 1.\r\n" );
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document.write( "Then to get the 4th term we take  and add\r\n" );
document.write( ", which is +1, times , to go up\r\n" );
document.write( "to 2.\r\n" );
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document.write( "etc., etc., etc.,...\r\n" );
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document.write( "So when n is odd, we go down by  to 1 from \r\n" );
document.write( "and when n is even, we go up by  to 2 from . \r\n" );
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document.write( "So to get the nth term we take  and add\r\n" );
document.write( " times ,\r\n" );
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document.write( "So the formula for the nth term, which we call  is\r\n" );
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document.write( "That will do for the formula, but maybe we want to write\r\n" );
document.write( "it a little differently. We change  to an improper\r\n" );
document.write( "fraction \r\n" );
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document.write( "Then we can factor out \r\n" );
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document.write( "Then we can change 'multiplying by ' to \r\n" );
document.write( "'dividing by 2' which is the same thing:\r\n" );
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document.write( "Edwin
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