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SeqLab
aₙ = a₁ + (n−1)d, Sₙ = (n/2)(2a₁ + (n−1)d).
In an arithmetic sequence, each term differs from the last by the same fixed amount (the common difference d) — 2, 5, 8, 11… adds 3 every step, so the nth term is just the start plus (n−1) steps of size d.
Simple interest, evenly-spaced seating rows, and any 'steady increase per period' scenario — like a savings plan that adds the same fixed amount every month — follow an arithmetic pattern.
aₙ (nth term)
29
aₙ = a₁ + (n−1)d
What you entered
nth term: a₁ + (n−1)d
2 + (10−1) × 3= 29Sum of first n terms
(10/2) × (2×2 + (10−1)×3)= 155Result
aₙ (nth term): 29
Starting at 2 with common difference 3, term 10 is 29, and the first 10 terms sum to 155.