Arithmetic Sequence Calculator
Enter the first term, common difference and n to get the nth term and the sum.
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nth term (aₙ)
nth term (aₙ)
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Sum of n terms (Sₙ)
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Arithmetic Sequence Calculator by TheCalcTools
How the Arithmetic Sequence Calculator works
Enter the first term, the constant difference between terms and how many terms you want.
The nth term adds (n − 1) differences to the first term.
The sum uses Gauss’s trick of pairing the first and last terms.
The formula
aₙ = a₁ + (n − 1)dSₙ = n(a₁ + aₙ) ÷ 2
Worked example
Using the default values shown in the calculator:
| First term (a₁) | 3 |
|---|---|
| Common difference (d) | 4 |
| Number of terms (n) | 10 |
- The sequence is 3, 7, 11, 15, …
- a₁₀ = 3 + 9 × 4 = 39.
- S₁₀ = 10 × (3 + 39) ÷ 2 = 210.
Result:
| nth term (aₙ) | 39.0000 |
|---|---|
| Sum of n terms (Sₙ) | 210.0000 |
Frequently asked questions
What is a common difference?
The fixed amount added to each term to get the next, for example 3, 7, 11, 15 has d = 4.
How did Gauss add 1 to 100 so quickly?
He paired 1 with 100, 2 with 99 and so on: 50 pairs each summing to 101, giving 5050.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.