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When adding up all the terms in an arithmetic sequence, you're calculating what's known as an arithmetic series sum. An arithmetic sequence is simply a list of numbers with a constant difference between each term. To calculate the sum of this kind of series, you can use a straightforward formula:

\[ S_n = n \cdot \frac{a_1 + a_n}{2} \]
where \( S_n \) is the sum of the first \( n \) terms, \( a_1 \) is the first term, \( a_n \) is the last term, and \( n \) is the number of terms in the series. This formula essentially multiplies the average of the first and last term by the number of terms. It's a quick method and a powerful one, as it saves you from needing to add up a potentially long list of numbers individually.

The common difference in an arithmetic series is the consistent amount that each term increases or decreases by from one to the next. Identifying the common difference is pivotal for understanding the nature of the series. For example, in the series given in the exercise, subsequent numbers decrease by 5, which we ascertain by subtracting one term from the next:

\[ 195 - 200 = -5 \]
This tells us the common difference is -5. It's crucial to recognize that the common difference can be positive or negative, leading to increasing or decreasing sequences, respectively. Your ability to identify and apply the common difference directly impacts your capacity to solve problems involving arithmetic series effectively.

Determining the number of terms in an arithmetic series is essential when you're trying to find its sum or understand its structure. There's a formula to find out the number of terms (\( n \)) based on the first term (\( a_1 \)), the last term (\( a_n \)), and the common difference (\( d \)):

\[ n = \frac{last\_term - first\_term}{common\_difference} + 1 \]
By using this formula, you can avoid the tedious process of counting each term one by one, especially in long series. For instance, with the series in the exercise, you calculate the number of terms as follows:

\[ n = \frac{65 - 200}{-5} + 1 \]
This equation makes it easy to deduce that there are 28 terms in the series. Remember, the '+1' in this formula accounts for including both the first and last terms in the count. Knowing how to find the number of terms is a fundamental skill for working with arithmetic series.