1. If a person invests in a tax-sheltered annuity, the money invested, as well as the interest earned, is not subject to taxation until withdrawn from the account. Assume that a person invests $2000 each year in a tax-sheltered annuity at 10 percent interest compounded annually. Let An represent the amount at the end of n years.
Find a recurrence relation for the sequence A0, A1,...
Find an initial condition for the sequence A0, A1,...
Find A1, A2, and A3.

2. Tell whether or not the recurrence relation below is a linear homogeneous recurrence relation with constant coefficients. Give the order of each linear homogeneous recurrence relation with constant coefficients.
an = 2nan - 1

3..Solve the given recurrence relation for the initial condition given.
an = an - 1 + n
a0 = 0

4. Solve the given recurrence relation for the initial condition given.
an = 7an - 1 - 10an - 2;
a0 = 5, a1 = 16

Solution Summary

The solution is comprised of detailed explanations of solving the recurrence relation.

Solve the following recurrencerelation:
a(n) = a(n-1) + 3(n-1), a(0) = 1
I know this should not be a difficult problem, but my main problem is in solvingthe problem when the coefficient of the a(n-1) term is 1. Also, when a summation is in the solution, I do not understand how to convert from a summation to a C(n,k)

Show that the Fibonacci numbers satisfy therecurrencerelation f_n = 5f_n-4 + 3f_n-5 for n = 5, 6, 7,..., together with the initial f_0 = 0, f_1 = 1, f_2 = 1, f_3 = 2, and f_4 = 3.
See the attachment for the full question.

Bob deposits quarters and dollar bills into a vending machine to buy snacks. Find a recurrencerelation for the number of ways he can deposit 25*n cents into the machine if the order matters. State therecurrencerelation and the initial conditions. Then use your recurrencerelation to find the number of ways Bob can deposit $3.

Suppose a sequence satisfies the given recurrence relation and initial conditions. Find an explicit formula for the sequence
s(subk)=-4s(subk-1)-4S(subk-2), for all integers k>or equal to 2
s(sub0)=0,S(sub1)=-1

1. Find the sequence for the recursive formula:
S_n = -s_n-1 + 9, s_0 = -3
(see the attachment for the full question)
2. True of False a_n = 2 is a solution to therecurrencerelation a_n = 2a_n-1 - a_n-2 with initial conditions a_0 = 2 and a_1 = 2.
a. True
b. False
3. Find a solution to therecurrencerelation:
a_

1. Pauline takes a loan of S dollars at an interest rate of r percent per month, compounded monthly. She plans to repay the loan in T equal monthly installments of P dollars each.
a) Let a(subscript n) denote the amount Pauline owes on the loan after n months. Write a recurrencerelation for a (subscript n).
b) Solve the rec

Please help with the following discrete math involving recurrencerelations, compound interest, polynomials, number of combinations and iteration.
14. Individual membership fees at the evergreen tennis club were $50 in 1970 and have increased by $2 per year since then. Write a recurrencerelation and initial conditions for

1. Find a functional equation and solve it for sequence of generating functions whose coefficients satisfy (assume and =1):
1.
2. Find a recurrencerelation and associated generating function for the number of n-digit ternary sequence that have the pattern "012" occurring for the first time at end of the sequence.