**Given:**

The sequence is
an=cosn
.

**Definition used:**

(1) The sequence
{an}
is increasing if
an<an+1
for all
n≥1
. That is,
a1<a2<a3<...
.

(2) The sequence
{an}
is decreasing and
an>an+1
for all
n≥1
. That is,
a1>a2>a3>...
.

(3) If the sequence is either increasing or decreasing, then the sequence is called monotonic; otherwise it is not monotonic.

(4) If
{an}
is the sequence with
m≤an≤M
for
m,M∈ℕ
, then the sequence is bounded.

**Calculation:**

The first five terms of the sequence is as follows.

{cosn}={cos1,cos2,cos3,cos4,cos5,...} ={0.54,−0.42,−0.99,−0.65,0.28,...}

Here,
a1>a2
and
a2>a3
but
a3<a4
and
a4<a5
.

Thus, it can be concluded that the sequence is neither increasing nor decreasing.

Therefore, by definition (3), the sequence is not monotonic.

Since
−1≤cosn≤1
and by definition (4), the sequence is bounded.

Hence, the sequence is bounded but not monotonic.