Find the general term of the sequence LaTeX: \displaystyle 1,- \frac{2}{5},\frac{4}{25},\ldots

The common ratio is LaTeX: \displaystyle r=\frac{a_2}{a_1}=- \frac{2}{5} . Using the first term and the common ratio gives LaTeX: \displaystyle a_n=1\left( - \frac{2}{5} \right)^{n-1}