Question

Converting Explicit formula to Recursive formula.

Answer 1

The formula
a(n) = 2 - 5(n-1)
is in the form
a(n) = a1 + d(n-1)

where
a1 = first term = 2
d = -5 = common difference

The first term is carried over to the recursive formula. We start with a1 = 2. The next term after that is found by subtracting 5 from the previous term. So
second term = (first term) - 5
third term = (second term) - 5
and so on

The recursive step would be 
a(n) = a(n-1)-5

So that's why the answer is choice C