document.write( "Question 847701: How would i write the recursive and explicit formula for this sequence:
\n" ); document.write( "2, 1/2, 1/4, 1/8, ....\r
\n" ); document.write( "\n" ); document.write( "I think the explicit formula is something like a[n]= 1/2n \n" ); document.write( "

Algebra.Com's Answer #510646 by jim_thompson5910(35256) $\"\"$ $\"About$

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The recursive formula would be \r
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\n" ); document.write( "\n" ); document.write( " $\"a_{n}$ \r
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\n" ); document.write( "\n" ); document.write( "This effectively says: \"To get the next nth term ( $\"a%5Bn%5D\"$ ), you have to multiply the previous term ( $\"a%5Bn-1%5D\"$ ) by $\"1%2F2\"$ . This means that to get the 10th term, you have to know the 9th term. To know the 9th term, you need the 8th, etc etc. So the recursive method is a lot of work if n is a large integer.\r
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\n" ); document.write( "\n" ); document.write( "The explicit formula is \r
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\n" ); document.write( "\n" ); document.write( " $\"a%5Bn%5D+=+2%281%2F2%29%5E%28n-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "where n starts at $\"n+=+1\"$ \r
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\n" ); document.write( "\n" ); document.write( "this is because any general geometric sequence that starts at $\"a\"$ and has a common ratio $\"r\"$ is $\"a%5Bn%5D+=+a%28r%29%5E%28n-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In this case, the first term is $\"a+=+2\"$ . The common ratio is $\"r+=+1%2F2\"$ \n" ); document.write( "

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