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# Other Useful Sequence Words Exercises

### Example 1

Determine if the sequence is increasing, decreasing, or neither.

an = 2n

### Example 2

Determine if the sequence is increasing, decreasing, or neither.

### Example 3

Determine if the sequence is increasing, decreasing, or neither.

an = (-1)n n2

### Example 4

Determine if the sequence is increasing, decreasing, or neither.

an = -n2

### Example 5

Determine if the sequence is increasing, decreasing, or neither.

### Example 6

Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.

### Example 7

Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.

an = 4 – n

### Example 8

Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.

an = (-1)n

### Example 9

Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.

an = n3

### Example 10

Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.

an = (-1)n2n

### Example 11

Determine if the statement is true or false. Explain your reasoning.

If a sequence has 5 ≤ an ≤ 6 for all n, then the sequence must converge.

### Example 12

Determine if the statement is true or false. Explain your reasoning.

The sequence 1,1,1,1,... is both convergent and bounded.

### Example 13

Determine if the statement is true or false. Explain your reasoning.

If a sequence diverges, the sequence is unbounded.

### Example 14

Determine if the statement is true or false. Explain your reasoning.

If a sequence is unbounded, that sequence diverges.

### Example 15

Determine if the statement is true or false. Explain your reasoning.

If a sequence converges, there is some value K such that Kan for all n.