To find: Formula for the general term
an of the sequence.

Answer

The general term
an of the sequence is
(−1)n+1n2n+1.

Explanation

Given:

The sequence is
{12,−43,94,−165,256,...}.

Here,
a1=12,a2=−43,a3=94,a4=−165 and a5=256.

Calculation:

The first term of the sequence can be written as
a1=121+1.

The second term of the sequence can be written as
a2=−222+1.

The third term of the sequence can be written as
a3=323+1.

The fourth term of the sequence can be written as
a4=−424+1.

The fifth term of the sequence can be written as
a5=525+1.

Here, it is observed that the numerator follows an alternative sequence with the general term
(−1)n+1n2 and the denominator follows a sequence with the general term
n+1.

Therefore, the formula for general term
an of the sequence is
(−1)n+1n2n+1.