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Write the nth term of the sequence as a function of n
1/2, -3/4, 9/8, -27/16, 81/32, -.....
1 Answer
- MarkLv 61 decade agoFavorite Answer
1/2, -3/4, 9/8, -27/16, 81/32, -.....
Notice first that the numerators are all powers of 3
Now see that the denominators are all powers of 2
Now see that the signs are alternating + and -
Hence
Un is of the form (- 3)^(n + k₁) / 2^(n + k₂)
A little trial and error soon leads to
Un = (- 3)^(n - 1) / 2^(n)
This might alternatively be written as
Un = ½ (- 3/2)^(n - 1)
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