Find the nth term and sum of an arithmetic sequence — free and instant.
An arithmetic progression is a sequence where each term increases by the same fixed amount (the common difference, d) from the one before it. Given the first term (a), the common difference (d), and which term number you want (n), this finds the nth term using aₙ = a + (n-1)d, and the sum of the first n terms using Sₙ = n/2 × (2a + (n-1)d).
Both are computed together since they're almost always asked about side by side — knowing a specific term rarely comes up without also wanting the running total up to that point.
Yes — a negative common difference gives a decreasing sequence, and both formulas work correctly either way.
Term numbers only make sense as positive whole numbers (1st term, 2nd term, and so on) — enter a whole number for n.
It comes from pairing the first and last term, the second and second-to-last, and so on — each pair sums to the same value (a + aₙ), and there are n/2 such pairs.