**Given:**

The sequence is
an=2+(0.86)n
.

**Definition used:**

If
an
is a sequence and
limn→∞an
exists, then the sequence
an
is said to be converges otherwise it is diverges.

**Result used:**

The sequence
{rn}
is converges to zero when
−1<r<1
.

That is,
limn→∞rn=0 if −1<r<1
.

**Calculation:**

Obtain the limit of the sequence to investigate whether the sequence is converges or diverges.

Compute
limn→∞an=limn→∞(2+(0.86)n)

limn→∞an=limn→∞(2+(0.86)n)=limn→∞(2)+limn→∞(0.86)n=2+limn→∞(0.86)n

Since
−1<0.86<1
and by using the result, the sequence
{(0.86)n}
is converges to zero.

Thus, the value of
limn→∞(0.86)n=0
.

Therefore,
limn→∞an=2
.

Since
limn→∞an
is exist and by using the definition of the sequence, it can be concluded that the sequence is converges to the limit 2.

Therefore, the sequence is converges to the limit 2.