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);
    }
}