The expression you've written is an arithmetic series:

$2 + 4 + 6 + \dots + 122$

This is an arithmetic sequence where:

• The first term $a = 2$
• The common difference $d = 2$

We need to find the sum of this sequence. First, we can determine the number of terms, $n$, in the sequence. The $n$-th term of an arithmetic sequence is given by:

$a_n = a + (n - 1) \cdot d$

Substituting $a = 2$, $d = 2$, and $a_n = 122$, we can solve for $n$:

$122 = 2 + (n - 1) \cdot 2$ $122 - 2 = (n - 1) \cdot 2$ $120 = (n - 1) \cdot 2$ $n - 1 = 60$ $n = 61$

So, there are 61 terms in the sequence.

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

$S_n = \frac{n}{2} \cdot (a + a_n)$

Substituting the values we have:

$S_{61} = \frac{61}{2} \cdot (2 + 122)$ $S_{61} = \frac{61}{2} \cdot 124$ $S_{61} = 61 \cdot 62$ $S_{61} = 3782$

So, the sum of the series is 3782.

Would you like further explanation or clarification on this? Here are some related questions you could explore:

1. How do you determine the sum of a sequence with a different common difference?
2. What happens if the sequence is geometric instead of arithmetic?
3. How do you find the sum of an infinite arithmetic series?
4. Can you find the sum of this sequence using an alternative method?
5. What are the properties of arithmetic sequences that might help solve similar problems?

Tip: In any arithmetic sequence, the sum formula works best when you first find the number of terms and ensure the sequence follows a consistent pattern.