**Given:**

The first five terms of the given sequence are
{−3,2,−43,89,−1627,...}

Here,
a1=−3,a2=2,a3=−43,a4=89 and a5=−1627
.

**Calculation:**

The first term of the given sequence is
a1=−3
.

The second term of the given sequence can be expressed as follows:

a2=−3−3⋅2=−3⋅(−23)

The third term of the given sequence can be expressed as follows:

a3=−3−3⋅4−3=−3⋅2⋅2(−3)⋅(−3)=−3(−23)2

The fourth term of the given sequence can be expressed as follows:

a4=−3−3⋅89 =−3⋅2⋅2⋅2(−3)⋅(−3).(−3) =−3⋅(−23)3

The fifth term of the given sequence can be expressed as follows:

a5=−3−3⋅16−3 =−3⋅2⋅2⋅2⋅2(−3)⋅(−3).(−3) =−3⋅(−23)4

Here, it is observed that the first term of the sequence is −3 and each term is
−23
times the previous term.

Therefore, the formula for the general term
an
of the sequence is
(−3)(−23)n−1
.