Question

Which of the following is the formula for the sequence whose grap14an42

Answer 1

Given:

We get the points (1, -1), (2, 1/4), (3, -1/9), (4, 1/16) and (5,0) from the given graph.

`a_1=-1,\text{ }a_2=(1)/(4),\text{ }a_3=-(1)/(9),\text{ }a_4=(1)/(16)\text{ and }a_5=0.`

Required:

We need to find the formula for the given sequence.

Step-by-step explanation:

The given sequence can be written as follows.

`a_1=-1=((-1)^1)/((1)^2)`
`a_2=(1)/(4)=((-1)^2)/((2)^2)`
`a_3=(-1)/(9)=((-1)^3)/((3)^2)`
`a_4=(1)/(16)=((-1)^4)/((4)^2)`
`a_5=(1)/(25)=((-1)^5)/((5)^2)=0.04=0`

In general,

`a_n=((-1)^n)/((n)^2)`

Final answer:

`a_n=((-1)^n)/((n)^2)`