Sequence...

**bearej50** · February 15th 2010, 08:21 AM

Find anfor this sequence:

5, 6, 7, 5, 6, 7, 5, 6, 7, ...

**Jhevon** · February 15th 2010, 09:12 AM

Originally Posted by bearej50

Find anfor this sequence:

5, 6, 7, 5, 6, 7, 5, 6, 7, ...

you can use a piece-wise definition: $a_n = \left \{ \begin{matrix} 5 & \text{ if } n \equiv 1 \bmod 3 \\ 6 & \text{ if } n \equiv 2 \bmod 3 \\ 7 & \text{ if } n \equiv 0 \bmod 3 \end{matrix} \right.$

are you familiar with the notation $n \equiv m \bmod 3$ ? It means $n = m + 3k$ for some integer $k$

**bearej50** · February 16th 2010, 05:48 PM

I am familiar with this notation but I was looking for a more generalized formula. For example, for the sequence: 5, 7, 5, 7, .... an = 6 - (-1)^(n+1)

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