Question

How do you write the expression for the nth term of the sequence given `1, 1/4, 1/9, 1/16, 1/25,...`?

Answer 1

`a_n=1/n^2`

Explanation:

`n: 1, 2, 3, 4, 5...`
`a_n: 1, 1/4, 1/9, 1/16, 1/25...`

`1^2=1, 2^2=4, 3^2=9`, etc.

`n: 1, 2, 3, 4, 5...`
`n^2: 1, 4, 9, 16, 25...`

`n: 1, 2, 3, 4, 5...`

`1/n^2: 1/1, 1/4, 1/9, 1/16, 1/25...`

`therefore a_n = 1/n^2`