Assignment:
Q1. 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in a tax-sheltered annuity, the money invested, as well as the interest earned, is not subject to taxation until withdrawn from the account.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.
Q2. 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
Q3..Solve the given recurrence relation for the initial condition given.
an = an - 1 + n
a0 = 0
Q4. Solve the given recurrence relation for the initial condition given.
an = 7an - 1 - 10an - 2;
a0 = 5, a1 = 16
Provide complete and step by step solution for the question and show calculations and use formulas.