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

How do you find the nth term of the sequence −1,2,−3,4,−5,6,...?
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Hofpoetb9
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 ${\left(-1\right)}^{n}$
Hence we can denote the ${n}^{th}$ term of the sequence by:
${u}_{n}={\left(-1\right)}^{n}n$