Find a formula for the general nth term an of the sequence a

Find a formula for the general (nth term an) of the sequence assuming the pattern of the first few terms continues {1, -2 / 3, 4 / 9, -8 / 27,}.

Solution

We can also write it as

(-1)^2*(3/2)^(1-1) + (-1)^3(3/2)^(1-2) + (-1)^4(3/2)^(1-3)

So General Form

(-1)ⁿ⁺¹(3/2)^1-n