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Arithmetic Sequence Term Calculator

Enter the first term, common difference, and position to find any term in an arithmetic sequence.

How it is calculated

The term at position n is the first term plus (n − 1) steps of the common difference.

aₙ = a₁ + (n − 1) × d

a₁ is the first term, d the common difference (it can be negative or a decimal, for a falling or fractional sequence) and n the position, counted from 1. The position must be a whole number of 1 or more: 0, negative or fractional positions give no result. The answer is shown to 4 decimals with thousands separators. Only one term is returned, not the whole list, and the sum of the terms is a different formula.

Worked example

Start at 5 and add 3 each time, and ask for the 20th term. Number of steps from the first term: 20 − 1 = 19. Total added: 19 × 3 = 57. Add to the first term: 5 + 57. The 20th term is 62.0000. The sequence begins 5, 8, 11, 14 and so on, so you can check that the term at position 4 is 5 + 3 × 3 = 14.

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Common mistakes

  • Multiplying n instead of n − 1 by the difference. The first term already is position 1, so only n − 1 steps are added.
  • Counting positions from 0. Here the first term is n = 1, and n = 0 gives no result.
  • Forgetting the sign of the difference. A sequence that goes down, such as 20, 17, 14, needs d = −3.
  • Entering a fractional position such as 2.5. A term exists only at whole positions.
  • Confusing the term with the sum of the first n terms. This tool gives the single value at position n.

About this calculator

An arithmetic sequence is a list of numbers where each term is found by adding the same fixed amount — the common difference, d — to the one before it, such as 3, 7, 11, 15 (common difference 4). Rather than counting forward term by term, the nth term can be found directly with the formula a_n = a₁ + (n − 1)d, where a₁ is the first term and n is the position you want.

Algebra courses introduce arithmetic sequences as the simplest kind of pattern-based reasoning before moving on to geometric sequences and series, and the same structure models any real-world quantity that changes by a constant amount each step — seating rows that each add a fixed number of extra seats, a savings plan that adds the same fixed deposit every period, or a simple interest schedule where the same amount of interest accrues each term.

With the first term, the common difference and the position n, the nth term a₁ + (n − 1)d is worked out for you.

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