`5, 13, 21, 29, 37, 45...` Decide whether the sequence can be represented perfectly by a linear or a quadratic model. If so, then find the model.

The given sequence is:

`5, 13 , 21 , 29, 37, 45`

To determine if it is a linear sequence, take the difference between the consecutive terms.

`5, 13, 21, 29, 37, 45`

 `vvv`  `vvv`  `vvv`  `vvv`  `vvv`

 `8`   `8`  `8`  `8`   `8`

Since the difference between consecutive terms are the same, the given sequence is linear.

To determine the model of a linear sequence, apply the formula

`a_n = a_1 + (n- 1)d`

where an is the nth term, a1 is the first term, d is the common difference, and n is any positive integer.

Plugging in the values of a1 and d, the formula becomes:

`a_n= 5 + (n-1)8`

`a_n=5 + 8n-8`

`a_n=8n - 3`

Therefore, the given sequence can be represented by a linear model which is `a_n=8n - 3` .

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