a) Find a recurrence relation for the balance B(k) owed at the end of k months on a loan at a rate of r if a payment P is made on the loan each month. [Hint: Express B(k) in terms of B(k −1) and note that the monthly interest rate is r ∕ 12.]b) Determine what the monthly payment P should be so that the loan is paid off after T months.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.