See the attached file for questioins
Thehonest
2.doc1. (4) Find the next four terms of the recursively-defined sequence:
2. (7) Let
,...
,
,
2
1
0
a
a
a
be defined by the formula, for all integers0
³
n
. Prove by induction that this sequence is a solution to the recurrence relation5
1
+
=
-
k
k
a
a
, for all integers1
³
k
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 an = 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.
2
1
-
-
-
=
k
k
k
a
ka
a
b.
2
1
2
-
-
+
=
k
k
k
b
b
b
c.
2
2
1
-
-
-
=
k
k
k
c
c
c
d.
2
1
-
-
+
=
k
k
k
d
d
d
p
e.
2
2
2
1
+
-
=
-
-
k
k
k
r
r
r
f.
1
10
-
=
k
k
s
s
g.
2
2
-
=
k
k
u
u
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):
