Final answer:
The general expression for the (n)th term in the sequence 1/2, -1/4, 9/8, -16/16, 25/32, -36/64, ........ is n^2 / 2^(n-1).
Step-by-step explanation:
To find a general expression for the (n)th term in the sequence 1/2, -1/4, 9/8, -16/16, 25/32, -36/64, ........, we can observe that the numerator is a perfect square and the denominator is a power of 2. Let's break down the sequence using patterns:
The numerator follows the pattern n^2, where n represents the term number. The denominator follows the pattern 2^n, where n represents the term number.
Therefore, the general expression for the (n)th term in the sequence is n^2 / 2^(n-1).