Arithmetic Sequence Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Arithmetic Sequence.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A sequence where each term is obtained from the previous by adding a fixed constant called the common difference d.
Add the same number each time — 2, 5, 8, 11, ... (add 3 each step). This is constant-rate growth.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Linear growth—the graph of an arithmetic sequence is a line.
Common stuck point: Use a_n = a_1 + (n-1)d, not a_1 + nd — off-by-one errors are very common. Sum: S_n = \frac{n(a_1 + a_n)}{2}.
Sense of Study hint: Subtract consecutive terms to find d, then verify by checking that the same d works for every pair.
Worked Examples
Example 1
easySolution
- 1 Use the arithmetic sequence formula to find the 20th term: a_n = a_1 + (n-1)d, where a_1 = 7, d = -3, n = 20.
- 2 Calculate: a_{20} = 7 + (20-1)(-3) = 7 - 57 = -50
- 3 Apply the partial sum formula: S_{20} = \frac{20}{2}(a_1 + a_{20}) = 10(7 + (-50)) = 10(-43) = -430
Answer
Example 2
mediumExample 3
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.