Arithmetic sequence — The sum of the first n terms (Sₙ)
Find the sum Sₙ of the first n terms.
Arithmetic sequence — The sum of the first n terms (Sₙ)
Arithmetic sequence · The same number is added to each term.
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Find the sum Sₙ of the first n terms.
- First term (a₁): Any finite number.
- Common difference (d): The amount added each time; it may be zero or negative.
- Term number (n): A positive whole number.
- Calculate: Result — The sum of the first n terms (Sₙ).
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Formula used for this answer:
Sₙ = n[2a₁ + (n − 1)d] ÷ 2
- a₁ = first term
- d = common difference (amount added each time)
- n = term number
- Sₙ = sum of the first n terms
Values substituted
First term (a₁) = 3 · Common difference (d) = 4 · Term number (n) = 5 → The sum of the first n terms (Sₙ) = 55
First term (a₁) = −2 · Common difference (d) = 0 · Term number (n) = 4 → The sum of the first n terms (Sₙ) = −8
Precision, signs, and limits
- n must be a positive whole number.
- Use n no greater than 1,000,000,000.
- The display removes unnecessary trailing zeros and uses scientific notation for very large or very small nonzero results. Calculation retains more precision than the display.
- Only the first six terms are previewed. The tool does not infer missing patterns, parse formulas, draw graphs, save history, or calculate infinite series.
- These inputs produce a result outside the supported numeric range. Use smaller values.
Frequently asked questions
First term (a₁)?
Any finite number.
Common difference (d)?
The amount added each time; it may be zero or negative.
Term number (n)?
A positive whole number.
Does the calculator find the rule from a list of terms?
No. Pattern inference can have many possible answers. Choose a defined sequence type and provide its first term and difference or ratio.