linear algebra - Determinant of a general Matrix

What are the steps to solve for the Determinant of this Matrix?
I thought about turning it into a lower triangular Matrix, but I can't figure how.

Thanks in advance.

Let $A =$

$\begin{pmatrix}1 & 1& 1 & \cdots & 1 \\ 1 & 1+a2 & 1 & \cdots & 1 \\ 1 & 1& 1 + a3 &\cdots & 1 \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ 1& 1 & 1 &\cdots& 1 + an \end{pmatrix}$