`1, 3, 1, 3, 1, 3, 1` Write an expression for the apparent nth term of the sequence. (assume that n begins with 1)

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`                                          

                     ...

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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