# Sum of Numbers (Arithmetic Series)

## Definition

The sum of an arithmetic sequence refers to the sum of consecutive terms in a sequence where the difference between consecutive terms is constant. You can calculate the sum of an arithmetic sequence using a specific formula.

To find the sum of the sequence from 1 to n, you can use the following formula:

(First term + Last term) × Number of terms / 2

a: Starting value

b: Ending value

c: Common difference

Common difference: The constant difference between consecutive terms in an arithmetic sequence.

### Mathematical Example

Let's find the sum of the sequence from 1 to 10:

a: Starting value = 1

b: Ending value = 10

c: Common difference = +1

Now, substituting these values into the formula:

### Advantages

The formula for the sum of an arithmetic sequence is simple and intuitive.

It allows for quick calculation of the sum of large numbers of terms.

It can be applied to general forms of arithmetic sequences.

### Disadvantages

This formula is only applicable to arithmetic sequences and cannot be used for other types of sequences.

The number of terms must be known to use the formula.

## Java Example

```
public class ArithmeticSeriesSum {
public static void main(String[] args) {
int start = 1;
int end = 10;
int commonDifference = 1;
int sum = (start + end) * ((end - start) / commonDifference + 1) / 2;
System.out.println("Sum from 1 to 10: " + sum);
}
}
```