Assignment:
Q1. Write the next four terms of the sequence: an - 3an-1 -1 for a0 = 1.
Q2. Find a recurrence relation with initial condition(s) satisfied by the sequence. Assume a0 is the first term of the sequence an = 2n
Q3. An employee joined a company in 1999 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the previous year's salary. What will be his/her salary in 2007?
Q4. If you deposit $10,000 in an account that yields 6% interest compounded yearly, what will be the balance at the end of 5 years?
Q5. What are the minimum number of moves it takes to solve the Tower of Hanoi puzzle with 5 disks?
Q6. True or False? Homogeneous linear recurrence equations are linear combinations of power functions.
Q7. True or False? an = 5a2n-1 - 3a2n-1 is a linear homogeneous linear recurrence relation.
Q8. Find a solution to the recurrence relation an = 3nan-1 , a0=2
Q9. True or False? The characteristic roots of a linear homogeneous recurrence relation with constant coefficients may be complex numbers.
Q10. Find the degree of the linear homogeneous linear recurrence relation: an = an-1 + 2an-3
Provide complete and step by step solution for the question and show calculations and use formulas.