I start by constructing the sequence xn.
See scratch work below:
First I tried different values of n. That resulted in the circled numbers: 1, 9, 36, 100, and 225. I noticed that all these numbers were perfect squares with the corresponding numbers 1, 3, 6, 10, 15, 21 as their square roots. These numbers form a sequence defined as xn above. I used this sequence to derive a way to find the summation of any n.