The recursive definition,is called a first-order difference equation and generates the seq...

The recursive definition,

is called a first-order difference equation and generates the sequence

A little simplification shows that the nth term of this sequence is

Now suppose that I represents the annual interest rate, but the interest is awarded in discrete packets, m times per year. Then the rate awarded during each compounding period is I/ m. Consequently, if the initial investment is P0, the balance is P0(1 + I/m) at the end of the first compounding period, P0(l+I/m)2 at the end of the second compounding period, and so on.

(a) Give a first-order difference equation with an initial condition that generates a sequence describing the balance in the account at the end of each compounding period.

(b) Find a formula for the nth term of the sequence generated by the first-order difference equation created in part (a).