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

Aug 14, 2017

The ${n}^{t h}$ term is ${\left(- 1\right)}^{n} n$

#### Explanation:

We have a sequence:

$- 1 , 2 , - 3 , 4 , - 5 , 6 , \ldots$

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

$1 , 2 , 3 , 4 , 5 , 6 , \ldots$

So we can denote the absolute value of the ${n}^{t h}$ term by $n$

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

$- , + , - , + , \ldots$

And we can achieve the correct sign for the ${n}^{t h}$ term by ${\left(- 1\right)}^{n}$

Hence we can denote the ${n}^{t h}$ term of the sequence by:

${u}_{n} = {\left(- 1\right)}^{n} n$