Marie takes out a $20,000 loan for a new car. The loan has an annual interest rate of 6% or, equivalently, a monthly interest rate of 0.5%. Each month, the bank adds interest to the loan balance (the interest is always 0.5% of the current balance), and then Marie makes a $200 payment to reduce the loan balance. Let B_n be the loan balance immediately after the nth payment, where B₀ = $20,000.

a. Write the first five terms of the sequence {B_n}.

b. Find a recurrence relation that generates the sequence {B_n}.

c. Determine how many months are needed to reduce the loan balance to zero.