Given:
We get the points (1, -1), (2, 1/4), (3, -1/9), (4, 1/16) and (5,0) from the given graph.
[tex]a_1=-1,\text{ }a_2=\frac{1}{4},\text{ }a_3=-\frac{1}{9},\text{ }a_4=\frac{1}{16}\text{ and }a_5=0.[/tex]
Required:
We need to find the formula for the given sequence.
Explanation:
The given sequence can be written as follows.
[tex]a_1=-1=\frac{(-1)^1}{(1)^2}[/tex][tex]a_2=\frac{1}{4}=\frac{(-1)^2}{(2)^2}[/tex][tex]a_3=\frac{-1}{9}=\frac{(-1)^3}{(3)^2}[/tex][tex]a_4=\frac{1}{16}=\frac{(-1)^4}{(4)^2}[/tex][tex]a_5=\frac{1}{25}=\frac{(-1)^5}{(5)^2}=0.04=0[/tex]
In general,
[tex]a_n=\frac{(-1)^n}{(n)^2}[/tex]
Final answer:
[tex]a_n=\frac{(-1)^n}{(n)^2}[/tex]
