Sequences & Series
Find the nth term and the sum of arithmetic and geometric sequences, with the formula and substitution shown. Try “sum of the first 20 terms of 3, 7, 11, …”.
Try an example:
What you can do with the Sequences & Series
Arithmetic and geometric sequences, nth term and sums.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. sum of the first 20 terms of 3, 7, 11, ...
How the Sequences & Series works
- Decide whether there is a common difference d (arithmetic) or common ratio r (geometric).
- Use aₙ = a₁ + (n − 1)d or aₙ = a₁rⁿ⁻¹ for the nth term.
- Use Sₙ = n/2 (a₁ + aₙ) or Sₙ = a₁(1 − rⁿ) ÷ (1 − r) for the sum.
Frequently asked questions
How can I tell arithmetic from geometric?
Arithmetic sequences add the same amount each time; geometric sequences multiply by the same amount.
When does an infinite geometric series converge?
When |r| < 1, and then the sum is a₁ ÷ (1 − r).
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