Arithmetic Sequence
Calculator
Results
- nth term
- 39
- Sum of terms
- 210
- Mean term
- 21
Results
| nth term | 39 |
| Sum of terms | 210 |
| Mean term | 21 |
formula-map diagram
- nth term
- 39
- Sum of terms
- 210
- Mean term
- 21
Formula map
Formula
aₙ = a₁ + (n − 1) × d, Sₙ = (n ÷ 2) × (a₁ + aₙ)= 39
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
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See all →Frequently asked questions
What inputs does this calculator take?+
The first term (a₁), the common difference (d) between consecutive terms, and either which term number (n) you want or how many terms to sum.
How is the nth term calculated?+
The nth term formula is aₙ = a₁ + (n-1)d. You start at the first term and add the common difference (n-1) times to reach term n.
How is the sum of the sequence calculated?+
The sum of the first n terms is Sn = n/2 × (a₁ + aₙ), or equivalently n/2 × (2a₁ + (n-1)d). It works by pairing the first and last terms, which always average to the same value.
What does a negative common difference mean?+
A negative d means the sequence is decreasing rather than increasing — each term is smaller than the one before it by a fixed amount.
Can d be a decimal or fraction?+
Yes, the common difference can be any real number, not just a whole number — arithmetic sequences work identically whether the step size is 1, 0.5, or -3.7.