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Which arithmetic sequence explicit formula would yield the following: $1$, $-1$, $1$, $-1$.

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    I'd rather say it is geometric, not arithmetic.2012-11-20

3 Answers 3

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None. A sequence $\,\{a_1,a_2,...\}\,$ is arithmetic iff $\,a_{n+1}-a_n=d=$constant, for any $\,n\geq 1\,$.

In this case it doesn't work, yet your sequence is a geometric one, since

$\frac{a_{n+1}}{a_n}=-1=\,\text{constant}$

and thus a general formula for the n-th element is $a_n=1\cdot(-1)^{n-1}=(-1)^{n-1}\,$

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    Indeed so, @Santiago. I wonder why someone thought my answer is incorrect/inappropriate and downvoted me...? Oh, well.2012-11-20
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$a_n = (-1)^{n+1}$ because for odd $n$, you get $1$ and for even $n$, $-1$

for $n \in N$ (I count $N$ as 1, 2,...)

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    The sequence is a1 = -1, a2 = 1, a3 = -1, a4 = 1.2012-11-20
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the sequence 1, (-1), (-1)(-1), (-1)(-1)(-1), ... is $(-1)^n$ for $n = 0,1,2,..$.

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    @SantiagoBueno, so what? also you're mistaken2012-11-20