1. For each of the sequences below, find the pattern that makes the sequence and then find the 5th and 6th terms.

a. 12, 14, 16, 18, ...
b. 4, 8, 16, 32, ...
c. 7, 15, 31, 63, ...
d. 16, 8, 4, 2, ...
e. 4, 9, 16, 25, ...
f. 14, 16, 20, 28, ...
g. 2.5, 3, 3.5, 4, ...
h. -4, 8, -16, 32...

2. Given the following formulas for the general term of a sequence, find the first three terms, t1, t2 and t3

a. < 5n − 2>
b. < 2n3 >
c. < n / 2 >
d. < 4n − 3>
e. 
f. < (n − 1)(n + 4 >

g. t n = n2 + 1

h. t n = 

3. Given the following first terms and the recursive function, find the next three terms.

 
First term
Recursive function
Next three terms
a.
t 1 = 5
t n+1 = t n + 2
5, _ , _ , _
b.
t 1 = 1
t n+1 = 3t n
1, _ , _ , _
c.
t 1 = 2
t n+1 = 3t n − 2
2, _ , _ , _
d.
t 1 = 3
t n+1 = (t n)2 + 2
3, _ , _ , _
e.
t 1 = 12
t n+1 =3 − t n
12, _ , _ , _

4. Evaluate the following sums:

5. Write the following sums in sigma notation:

a. 12 + 13 + 14 + 15 +16 + 17

b. 2t3 +2t4 +2t5 +2t6

c. 9 + 16 + 25 + 36

d. 4 + 6 + 8 + 10 + 12 + 14

e. -3 + 6 − 9 + 12 − 15 + 18 − 21

f.  17 + 26 + 37 + ... + 145

6. Draw a graph of the following sequences and say whether the sequence is:

(i) increasing, decreasing or oscillating
(ii) Convergent or divergent (if it is convergent, give the limit)

a
b
< n+ 5 >
c
d
<(-1)n(n + 1)>
e
< n2 − 3n >
f
t(n) = 3