1. For each of the sequences below, find the pattern that makes the sequence and then find the 5th and 6th terms.
a. 2, 4, 6, 8, ...
|
b. 3, 6, 12, 24, ...
|
c. 3, 7, 15, 31, ...
|
d. 18, 9, 4.5, 2.25, ...
|
e. 1, 4, 9, 16, ...
|
f. 4, 6, 10, 18, ...
|
g. 2.5, 3, 3.5, 4, ...
|
h. 2, -4, 8, -16, ...
|
i. x, x3, x5, x7, ... |
j. -10, -7, -4, -1,...
|
k. 1, 8, 27, 64, ...
|
l. 2, 3, 5, 7, ...
|
2. Given the following formulas for the general term of a sequence, find the first three terms, t1, t2 and t3
a. < 2n + 1 >
|
b. < n2 >
|
c. < 2n >
|
d. < 3n − 5 >
|
e.
|
f. < (n − 2)(n + 3 >
|
g. t n = n3 + 2 |
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 = 4
|
t n+1 = t n + 3
|
4, _ , _ , _ |
b.
|
t 1 = 2
|
t n+1 = 2t n
|
2, _ , _ , _ |
c.
|
t 1 = 3
|
t n+1 = 2t n − 3
|
3, _ , _ , _ |
d.
|
t 1 = 1
|
t n+1 = (t n)2 + 1
|
1, _ , _ , _ |
e.
|
t 1= 10
|
t n+1 =2 − 2t n
|
10, _ , _ , _ |