The question asks to calculate the sum of an arithmetic series:
$2 + 4 + 6 + \dots + 60$

This is an arithmetic series where:

• The first term $a = 2$
• The common difference $d = 2$
• The last term $l = 60$

Steps to solve:

1. Determine the number of terms, $n$:
   The formula to find the $n$-th term of an arithmetic series is:
   $a_n = a + (n-1) \cdot d$
   Plugging in the values: $60 = 2 + (n-1) \cdot 2$ $60 - 2 = (n-1) \cdot 2$ $58 = (n-1) \cdot 2$ $n-1 = 29$ $n = 30$

   So, the number of terms is $n = 30$.

2. Use the sum formula for an arithmetic series:
   The sum of an arithmetic series is given by: $S_n = \frac{n}{2} \cdot (a + l)$ Substituting the known values: $S_{30} = \frac{30}{2} \cdot (2 + 60)$ $S_{30} = 15 \cdot 62$ $S_{30} = 930$

Final Answer:

The sum of the arithmetic series is $930$.

Do you need more details or have any questions?

Here are 5 follow-up questions to expand your understanding:

1. How would the solution change if the last term was 62 instead of 60?
2. What if the common difference was 3 instead of 2, how would you approach it?
3. Can you derive the sum if only the first term and common difference are given, without knowing the last term?
4. What is the sum of the first 100 terms of this arithmetic series?
5. How would the sum formula differ if the sequence were geometric instead of arithmetic?

Tip: In arithmetic sequences, always start by checking the number of terms and the common difference; these are key for using the sum formula.