Let us start with the sequence `-1,1,-1,1,-1,1,...` The `n`th term of this sequence is `(-1)^n` (for odd `n` we get `-1` while for even `n` we get `1`) If we add `2` to each term of this sequence we get

`2-1,2+1,2-1,2+1,...=1,3,1,3,...`

which is exactly our sequence. Therefore, the `n`th term of our sequence is

`a_n=(-1)^n+2` ...

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Let us start with the sequence `-1,1,-1,1,-1,1,...` The `n`th term of this sequence is `(-1)^n` (for odd `n` we get `-1` while for even `n` we get `1`) If we add `2` to each term of this sequence we get

`2-1,2+1,2-1,2+1,...=1,3,1,3,...`

which is exactly our sequence. Therefore, the `n`th term of our sequence is

`a_n=(-1)^n+2`

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