In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
The first five terms of the recursively defined sequence are .
The given recursively defined sequence is:
The first term is .
Now substitute 2 for n in the given formula to get the second term,
Similarly substitute 3, 4 for n in the given formula to get the third and fourth term,
Now substitute 5 for n in the given formula to get the 5th term,
Therefore, the first five terms are .
Education IRA: On January 1, 1999, John’s parents decided to place $45 at the end of each month into an Education IRA.
(a) Find a recursive formula that represents the balance at the end of each month if the rate of return is assumed to be 6% per annum compounded monthly.
(b) How long will it be before the value of the account exceeds $4000?
(c) What will be the value of the account in 16 years when John goes to college?
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