What is the explicit formula of: a. 1/3, -2/9, 4/27, -8/81also, how do you find it?

This looks like a Geometric Sequence in which you get the next term by multiplying by a constant factor

- 2/9 / 1/3  = -2/9 * 3 = -2/3
4/27  / -2/9  = 4/27 + 9/-2 =  -2.3 also  
and last term divided by 4/27 gives -2/3 as well   so it is a GS  with common ratio (r) = -2/3.

nth term  an = a1r^(n-1)   where a1 = frst term and r = common ratio.

so here it is  1/3 (-2/3)^(n-1)  < explicit formula