Arithmetic Sequence Calculator – nth Term and Sum
Find the nth term and sum of the first n terms from a starting value and constant difference.
Formula
aₙ = a₁ + (n−1)d; Sₙ = n[2a₁ + (n−1)d]/2.
nth term ≈ (2)+((10)-1)×(3) · Sum of first n terms ≈ (10)×(2×(2)+((10)-1)×(3))÷2
How to use
- Enter the first term a₁.
- Enter the common difference d, which may be negative.
- Choose a positive integer n and read aₙ and Sₙ.
Examples
- For a₁=2, d=3 and n=10, a₁₀=29 and S₁₀=155.
Frequently asked questions
Does n start at zero?
No. The first term is indexed by n=1.
Can the difference be zero?
Yes. Every term then equals the first term.
Does this list every term?
No. It returns the requested term and finite sum, not an expanded list.
Sources
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