To find the first three terms of the sequence defined by [tex]\(a_n = \frac{(-1)^n}{n+1}\)[/tex], we will plug in the values of [tex]\(n = 1\)[/tex], [tex]\(n = 2\)[/tex], and [tex]\(n = 3\)[/tex] into the given formula:
1. For [tex]\(n = 1\)[/tex]:
[tex]\[
a_1 = \frac{(-1)^1}{1 + 1} = \frac{-1}{2} = -0.5
\][/tex]
2. For [tex]\(n = 2\)[/tex]:
[tex]\[
a_2 = \frac{(-1)^2}{2 + 1} = \frac{1}{3} \approx 0.33333
\][/tex]
3. For [tex]\(n = 3\)[/tex]:
[tex]\[
a_3 = \frac{(-1)^3}{3 + 1} = \frac{-1}{4} = -0.25
\][/tex]
Therefore, the first three terms of the sequence are:
[tex]\[
a_1 = -0.5, \quad a_2 = 0.33333, \quad a_3 = -0.25
\][/tex]
