Question

Find the nth term of the sequence defined by the explicit formula a_n = ((-1)^n * n^2) / (n + 1).

Answer 1

To find the nth term of the sequence defined by the explicit formula a_n = ((-1)^n * n^2) / (n + 1), substitute the value of n into the formula and simplify.

Step-by-step explanation:

The explicit formula for the sequence is an = ((-1)n * n2) / (n + 1). To find the nth term of the sequence, substitute the value of n into the formula:

an = ((-1)n * n2) / (n + 1)

For example, if you want to find the 5th term, substitute n = 5:

a5 = ((-1)5 * 52) / (5 + 1) = ((-1) * 25) / 6 = -25/6.

Therefore, the 5th term of the sequence is -25/6.