Deduce the $\displaystyle rth$ term of the series $\displaystyle 5+55+555+5555+....$ can be expressed as $\displaystyle \frac{5}{9}(10^r-1)$.

Hence find, in terms of $\displaystyle k$, an expression for the sum of the first $\displaystyle k$ terms of the series $\displaystyle 5+55+555+5555+....$

I tried to find the common difference or common ratio to see if it is an arithmetic or geometric progression but it didnt work out....