Sum of an Arithmetic Series

📊 beginner

$$S_n = \frac{n}{2}(a_1 + a_n)$$

Calculates the sum of the first $n$ terms of an arithmetic progression.

Variables & Units

$S_n$

Sum of $n$ terms

Unit: Dimensionless

$a_1$

First term

Unit: Dimensionless

$a_n$

$n$-th term

Unit: Dimensionless

Key Information

📐 Derived From

Averaging the first and last terms and multiplying by number of terms.

💡 Example

Sum of numbers from 1 to 100.

🔧 Applications

Financial math and pattern analysis.

⚠️ Constraints

The difference between consecutive terms must be constant.

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