Arithmetic Sequence nth Term
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
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An arithmetic sequence climbs (or falls) by the same amount every step, so the nth term is just the first term plus (n − 1) copies of the common difference d. Theater rows work this way: if row 1 has 20 seats and each row adds 3 more, row 12 has 20 + 11 × 3 = 53 seats.
Run it backward to locate a value: with a₁ = 5 and d = 4, the term equal to 45 sits at n = (45 − 5)/4 + 1 = 11. If that comes out fractional, the value simply never appears in the sequence.
Arithmetic Sequence nth Term
Where
- = nth term
- = First term
- = Term number
- = Common difference
Missing one of these? Work it out first, then come back
- nth term — Geometric Sequence nth Term, Arithmetic Series Sum
- First term — Arithmetic Series Sum, Geometric Sequence nth Term
- Term number — Geometric Sequence nth Term, Arithmetic Series Sum
- Common difference — Arithmetic Series Sum, Geometric Sequence nth Term