Answer
1st term: -1; 2nd term: $\frac{1}{4}$ 3rd term: $\frac{-1}{9}$ 4th term: $\frac{1}{16}$ 100th term: $\frac{1}{10,000}$
Work Step by Step
To find the nth term of sequence, plug in a number for n. So, for the first term, plug in 1 for n, for the second term, plug in 2 for n, and so on. In this case:
1. For the first term: $\frac{(-1)^{n}}{n^{2}}$; plug in 1 for n: $\frac{(-1)^{1}}{1^{2}}$ = -1.
2. Repeat this pattern for the next three terms, plugging in 2, 3, and 4 for n and solving.
3. For the 100th term: $\frac{(-1)^{n}}{n^{2}}$; plug in 1000 for n: $\frac{(-1)^{1000}}{1000^{2}}$ = $\frac{1}{10,000}$
