MathNet 2012 Question 38

Find a triple $(l, m, n)$ ($1 \lt l \lt m \lt n$) of positive integers such that $\sum_{k=1}^{l} k$, $\sum_{k=l+1}^{m} k$, $\sum_{k=m+1}^{n} k$ form a geometric sequence in order. (posed by Tao Pingsheng)