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

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Answer 1 · 2017-08-14T13:08:02

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

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:

$u_n = (-1)^n n$

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