Question

How do you find the nth term of the sequence `-1,2,-3,4,-5,6,...`?

Answer 1

The `n^(th)` term is `(-1)^n n`

Explanation:

We have a sequence:

`-1,2,-3,4,-5,6,...`

Firstly we note that the absolute value of the terms increment by unity. so we can denote the absolute value as:

`1,2,3,4,5,6 , ...`

So we can denote the absolute value of the `n^(th)` term by `n`

Secondly, we note that the signs of each term alternates, and we start with a negative term

`-,+,-, +, ...`

And we can achieve the correct sign for the `n^(th)` term by `(-1)^n`

Hence we can denote the `n^(th)` term of the sequence by:

`u_n = (-1)^n n`