Final answer:
The formula for the nth term of the sequence described in the question is 2n², derived from pairing terms and simplifying using series expansions.
Step-by-step explanation:
The question asks to find the formula for the nth term of a certain sequence. The provided expression in the box hints at a pattern of summing terms in pairs from opposite ends of the sequence, which reduces to simply multiplying n by itself (n²), indicating that the formula for the nth term of the sequence could be related to square numbers.
To find the specific form of the nth term, we can use the concept of series expansions. With the given hint, we perform manipulations to pair the first and last term, the second and second to last, and so on, which simplifies to 2n² when we take into account the subtraction of (n − 1) and (n − 3) from the last and penultimate terms, respectively. Therefore, the formula for the nth term is 2n².