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Arithmetic Sequence nth Term

an=a1+(n−1)da_n = a_1 + (n - 1) d

Units aren’t used in this calculation: every value is a plain number.

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Worked example: 2, 5, 8, ... 10th term → 29. Press Try an example to run it live, then adjust anything.

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Where Arithmetic Sequence nth Term fits

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See also

Geometric Sequence nth Term: Both use nth term and first term.Arithmetic Series Sum: Both use first term and common difference.Geometric Series Sum: Both use first term.Infinite Geometric Series: Both use first term.
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Arithmetic Sequence nth Term explained

da1ann

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 formula

an=a1+(n−1)da_n = a_1 + (n - 1) d
Where
  • ana_n= nth term
  • a1a_1= First term
  • nn= Term number
  • dd= Common difference
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Arithmetic and geometric sequences

5 formulasThe nth term and the sum for both arithmetic and geometric progressions, including the infinite sum that converges.

Revised 31 October 2026
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formula.expert. (2026, October 31). Arithmetic Sequence nth Term Formula & Calculator. https://formula.expert/solvers/arithmetic-nth-term

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