See the attached file for questioins

1.      (4) Find the next four terms of the recursively-defined sequence:

2.      (7) Let  be defined by the formula, for all integers.  Prove by induction that this sequence is a solution to the recurrence relation , for all integers  where a₀ = -1.

3.      (4) f(a) =  . Express this polynomial in a recursively.

4.      (4) The producity of a worker at a scrapbook sticker company increased as an Arithmetic Sequence (Progression) over a period of 7 days. That is, on day n she produced a_n = a₁ + (n – 1)d stickers. If a₇ = 160 and d = 10 what is the total number of stickers she produced over the period of 7 days?

(6) Tom decided to do an exercise involving the Fibonacci and Geometric sequences. He will be pouring liquid into a container. For the first 10 days he will pour in liters of liquid corresponding to the Fibonacci sequence, starting with 1 liter on the first day and 1 liter on the second day. He will use day 10 as the first day of his Geometric sequence and for the next 3 days he will increase the number of liters he pours in by 10% of the previous day. How many liters will he pour into the container on day 13?

5.      (7) Which of the following are second-order linear homogeneous recurrence relations with constant coefficients?  Place “yes” against all that are. If anyone is not give a reason.

a. 

b. 

c. 

d. 

e. 

f. 

g. 

6.      (9) Find a closed form expression that is a solution to the sequence defined by the following recurrence relation and initial conditions (use the method of characteristic equation):

7.      (9) Find a solution for the following recurrence relation and initial conditions (use the method of characteristic equation):