Which arithmetic sequence explicit formula would yield the following: $1$, $-1$, $1$, $-1$.
Arithmetic sequence explicit formula.
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arithmetic
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4I'd rather say it is geometric, not arithmetic. – 2012-11-20
3 Answers
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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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0Indeed 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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0The 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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1@SantiagoBueno, so what? also you're mistaken – 2012-11-20