Question

write the second term of the sequence.
$a_n = \frac{(-1)^{n + 1}}{4^n - 1}$
the second term of the sequence is \\(\square\\). (type an integer or a simplified fraction.)

Explanation:

Step1: Identify n for the second term

For the second term, \( n = 2 \).

Step2: Substitute n = 2 into the formula

Substitute \( n = 2 \) into \( a_{n}=\frac{(-1)^{n + 1}}{4^{n}-1} \).
First, calculate the numerator: \( (-1)^{2 + 1}=(-1)^{3}=-1 \).
Then, calculate the denominator: \( 4^{2}-1 = 16 - 1=15 \).
So, \( a_{2}=\frac{-1}{15}=-\frac{1}{15} \).

Answer:

\(-\frac{1}{15}\)