#### Answer

The sequence is arithmetic.
Recursive formula : A(n) = A(n - 1) - 15 ; A(1) = 46
Explicit formula : A(n) = 46 + (n - 1)(-15)

#### Work Step by Step

The sequence is arithmetic because there is a common difference between all the terms which is -15
Explicit formula- For this formula we need to find the d value and A(1) and we can find the d value by subtracting the second term from the first.
D = 31 - 46
D= - 15
A(1) = 46 ; We can now form the equation A(n) = 46 + A(n - 1)(-15)
Recursive- For this formula, we need the common difference and A(1) and since the common difference is the same as the d value in the explicit formula, we can use that.
Common difference = -15
A(1) = 46; We can now form the equation A(n) = A(n - 1) - 15 ; A(1) = 46