Question

Find the explicit formula for the nth term of the 2/9,0,2/9,0,......

Answer 1

The odd-numbered terms are $\dfrac19+\dfrac19$, while the even-numbered terms are $\dfrac19-\dfrac19$, so one formula for the sequence is

$a_n=\dfrac19\left(1+(-1)^{n+1}\right)$

where $n\ge1$.