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Arithmetic and Geometric Sequence Calculator

Find the nth term and the sum of an arithmetic or geometric sequence, with the first terms listed.

Rules last checked 25 October 2026Every step shown

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Term 10

39

Sum of 10 terms
210
The sequence
3, 7, 11, 15, 19, 23, 27, 31, 35, 39

The arithmetic sequence 3, 7, 11, 15, … has term 10 = 39 and its first 10 terms add up to 210.

How it's worked out

  1. Term 10a + (n − 1)d = 3 + 9 × 439
  2. Sumn ÷ 2 × (2a + (n − 1)d) = 10 ÷ 2 × (6 + 36)210

The formulas

Arithmetic: aₙ = a + (n − 1)d, Sₙ = n ÷ 2 × (2a + (n − 1)d) · Geometric: aₙ = a × rⁿ⁻¹, Sₙ = a(1 − rⁿ) ÷ (1 − r)

Worked examples

3, 7, 11, …: the 10th term is 3 + 9 × 4 = 39 and the first 10 add up to 210. 3, 6, 12, …: the 10th term is 3 × 2⁹ = 1,536 and the first 10 add up to 3,069.

Questions people ask

What is an arithmetic sequence?

One where you add the same number each time: 3, 7, 11, 15… has a common difference of 4.

What is a geometric sequence?

One where you multiply by the same number each time: 3, 6, 12, 24… has a common ratio of 2.

What is the sum to infinity?

For a geometric sequence with a ratio between −1 and 1, the sum gets closer and closer to a / (1 − r). For 3, 1.5, 0.75… it's 6.

Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem