Arithmetic Series
Sum of an arithmetic sequence.
Key idea
Sum of an arithmetic sequence.
In depth
An arithmetic series sums terms with a constant difference. Sₙ = n(a₁ + aₙ)/2: the average of the first and last term times the number of terms. Gauss pairing explains why.
Worked example
1 + 2 + ... + 100 = 100(1 + 100)/2 = 5050.
Formula
Real-world uses
- Totalling a staircase of seats or the savings from a plan that adds a fixed sum each month
Common mistake
Using the wrong number of terms; check n by (last − first)/d + 1.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Arithmetic Series?
Sum of an arithmetic sequence. It is a topic at the advanced level in Algebra.
What is the formula for Arithmetic Series?
The key formula is Sₙ = n(a₁+aₙ)/2.
Where is Arithmetic Series used in real life?
Real-world examples: Totalling a staircase of seats or the savings from a plan that adds a fixed sum each month.
What should I learn before Arithmetic Series?
Make sure you are comfortable with Natural Logarithm, the previous topic in Algebra.
What is a common mistake with Arithmetic Series?
Using the wrong number of terms; check n by (last − first)/d + 1.
How can I practise Arithmetic Series?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Arithmetic Series?
Move on to Geometric Series next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.