# How do you get a formula of the nth term for this sequence:1, 1/2, 3, 1/4, 5, 1/6...?

##### 1 Answer
Nov 12, 2015

One possibility is
$\textcolor{w h i t e}{\text{XXX}} {a}_{n} = {n}^{{\left(- 1\right)}^{n - 1}}$

#### Explanation:

The sequence $1 , 2 , 3 , 4 , 5 , 6 , \ldots$ is clearly just ${a}_{n} = n$
but we want the reciprocal of all even numbered terms and one way to do this is to use the alternating nature of
$\textcolor{w h i t e}{\text{XXX}} {\left(- 1\right)}^{n - 1}$
(noting that we need to subtract $1$ from the exponent $n$ so that it is the even and not the odd terms for which we take the recipocal.)