Question

Is the sequence "7, 3, 13, 23,..." arithmetic? If so, what is the explicit formula?

Answer 1

I think you are missing an initial `-` sign.

The series `-7, 3, 13, 23` is arithmetic with initial term `-7` and common difference `10`:

`a_n = -7+10(n-1) = 10n-17`

Explanation:

Arithmetic sequences have the same difference between successive terms.

In our case (assuming I'm correct about the missing `-` sign), the difference between any two successive terms is `10`.

The general formula for the `n`th term of the sequence may be written in the form:

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

where `a_1` is the first term and `d` the common difference.

In our case, the first term is `a_1 = -7`, common difference `d=10` and the formula becomes:

`a_n = -7+10(n-1) = 10n-17`