Question

Use math notation to describe the following sequence:
1, -1, 1, -1,...

Answer 1

The math notation to the given sequence is
`a_n=(-1)^(n+1)` for n=1,2,3,... is verified and it is true

Explanation:

Given sequence is 1,-1,1,-1,...

Let
`a_1=-1,a_2=1,a_3=-1,a_4=-1,...`

To find the math notation for the given sequence :

`a_n=(-1)^(n+1)` for n=1,2,3,... verify that it is true or not

Put n=1 in the above equation we get

`a_1=(-1)^(1+1)`

`=(-1)^2`

Therefore
`a_1=1`

Put n=2 in the
`a_n=(-1)^(n+1)` equation we get

`a_2=(-1)^(2+1)`

`=(-1)^3`

Therefore
`a_2=-1`

Put n=3 in the
`a_n=(-1)^(n+1)` equation we get

`a_3=(-1)^(3+1)`

`=(-1)^4`

Therefore
`a_3=1`

and so on

Therefore the math notation to the given sequence is
`a_n=(-1)^(n+1)` for n=1,2,3,... is verified and it is true