The given formula is for the sum of an arithmetic series:

$S_n = \frac{n}{2} \left( 2a + (n - 1)d \right)$

where:

• $S_n$ is the sum of the first $n$ terms,
• $a$ is the first term,
• $d$ is the common difference between terms,
• $n$ is the number of terms.

You provided that $a = 1$ and $d = 1$. So, the formula becomes:

$S_n = \frac{n}{2} \left( 2(1) + (n - 1)(1) \right)$

Simplify:

$S_n = \frac{n}{2} \left( 2 + (n - 1) \right)$

$S_n = \frac{n}{2} \left( n + 1 \right)$

Now, you need to find $n$ based on the value of $S_n$ you have. Can you provide the sum $S_n$ for which you want to solve $n$?