Series Worksheets
Free PDF · Problems + answer key · Instant download
Easy
10 problemsMedium
20 problemsHard
20 problemsMixed
30 problemsFree printable series worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from term aₙ of an arithmetic series at the easy level through to convergence and sum of an infinite geometric series at the advanced level.
What is series?
A series is the sum of the terms in a sequence. For example, if you have the sequence 2, 4, 6, 8, the corresponding series is 2 + 4 + 6 + 8 = 20. Series can be finite with a set number of terms, or infinite where terms continue without end.
Understanding series is essential for calculus, where infinite series help represent functions and solve complex problems. Series appear in finance when calculating loan payments or investment growth, in physics when modeling wave behavior, and in computer science for algorithm analysis. They provide a foundation for understanding how repeated additions build toward a total value.
Pick a difficulty
Click any level to open the generator with that difficulty pre-selected.
Beginner
Generate →- Concepts
- Term aₙ of an arithmetic series
- Range
- a₁: 1–10, d: 1–6, n: 4–10
- Steps
- 2 steps
- Example
- aₙ = a₁ + (n − 1)d
Easy
Generate →- Concepts
- Sum Sₙ of an arithmetic series
- Range
- a₁: 1–10, d: 1–6, n: 5–15
- Steps
- 2 steps
- Example
- Sₙ = n/2·(2a₁ + (n − 1)d)
Medium
Generate →- Concepts
- Sum of a finite geometric series
- Range
- a₁: 1–6, k: 2–4 or 1/2, 1/3, n: 4–8
- Steps
- 2 steps
- Example
- Sₙ = a₁·(kⁿ − 1)/(k − 1)
Hard
Generate →- Concepts
- Convergence and sum of an infinite geometric series
- Range
- a₁: 1–12, k convergent |k|<1 or divergent |k|≥1
- Steps
- 2–3 steps
- Example
- S = a₁/(1 − k) når |k| < 1
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