At which height an element belongs Suppose there is a triangle as follows where first row contains $1$ element,
the second row contains $2$ elements and so on like below diagram.

$$
\begin{array}{rccccccccc}
&amp; &amp; &amp;1&amp; &amp; &amp; \\
&amp; &amp;2&amp; &amp;3&amp; &amp; \\
&amp;4&amp; &amp;5&amp; &amp;6&amp; \\
&amp; &amp; &amp; \vdots&amp; &amp; &amp; \\
\end{array}
$$

Then what will be the row number of an element?

For example for $n=3$ the row number is $2$.
Let, $$x=\frac{\sqrt{8n+1}-1}{2}$$
Then the row the $n$-th number will be in is given by;
$$R_n=n-\frac{\lceil x \rceil(\lceil x \rceil-1)}{2}$$
Since in the question you stated that $n^{th} $ row contains n elements , the answer is , well....

Edit : Since you have edited the question , the new answer is : 

Hint:

The first element in the $n^{th} $ row is given by $1+\frac{(n-1)n}{2} $ and the last element is given by $1+\frac{(n-1)(n+2)}{2}.$ 

Can you figure out the rest ?