Geometric sequence term

Type the first term a₁, the ratio q and the index n. aₙ = a₁×qⁿ⁻¹. 2, 3 and 4 give 54. 1, 2 and 5 give 16. 5, 0.5 and 3 give 1.25.

n goes through max(1, the integer part of (n)). Typed 1.9 becomes 1. The result is raw, without trimming decimals. 5, 0.5 and 3 show 1.25.

Input data

Results

Enter data and click Calculate.

How it works

The nth geometric term is the first term times the ratio to the power n−1. The calculator computes a₁×qⁿ⁻¹. 2, 3 and n = 4 give 2×27 = 54. The result goes in raw, not a trimmed decimal string.

The fields are a₁, q and n. The IDs stay a, b, c. 1, 2 and 5 give 16. 5, 0.5 and 3 give 1.25, because 5×0.25. n is cut with floor and never drops below 1.

Typed n = 0 or n = 0.4 becomes 1, so you get a₁ back. n = 4.9 becomes 4. q = −2 with a₁ = 3 and n = 4 would give −24. That is the its own card.

The nth arithmetic term adds r. The geometric series sum is on the neighbouring page and adds terms, it does not return one aₙ.

The header units switch does not multiply anything. 2, 3, 4 stay 54 whatever the label says.

2, 3 and 4 give 54. 1, 2 and 5 give 16. 5, 0.5 and 3 give 1.25.

Formula

aₙ = a₁ × qⁿ⁻¹, n = max(1, floor(n))

How to use

  1. Type a₁, q and n, for example 2, 3 and 4.
  2. Click Calculate. The nth term is 54.
  3. 1, 2 and 5 give 16. 5, 0.5 and 3 give 1.25.
  4. n = max(1, the integer part of (n)). Typed 1.9 counts as n = 1.
  5. The sum of that sequence lives on the geometric series card.

2, 3 and n = 4 give 54

aₙ = a₁×qⁿ⁻¹. n = max(1, the integer part of (n)). 2, 3 and 4 give 54. 1, 2 and 5 give 16. 5, 0.5 and 3 give 1.25.

geometric
A constant ratio q. 2 and 3 at n = 4 give 54. 1 and 2 at n = 5 give 16.
ratio
Field q. 0.5 with a₁ = 5 and n = 3 gives 1.25. A negative q flips the sign.
term
Index n after floor, never below 1. n = 1 returns a₁.

Examples

Example 1

  • a₁ = 2
  • q = 3
  • n = 4

54

What is the 4th term with a₁ = 2 and q = 3? 54. 2×3³.

Example 2

  • a₁ = 1
  • q = 2
  • n = 5

16

What is the 5th term with a₁ = 1 and q = 2? 16.

Example 3

  • a₁ = 5
  • q = 0.5
  • n = 3

1.25

What is the 3rd term with a₁ = 5 and q = 0.5? 1.25. A raw JS fraction.

Related calculators

Arithmetic sequence term

Arithmetic sequence term: the first term a₁, the common difference r and the index n.

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Geometric series sum

Geometric series sum calculator: the first term, the ratio, and the term count.

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Common questions

What is the 4th term with 2 and q = 3?

54. 2×3³ = 54.

What does a geometric nth term mean?

Term number n in a sequence with a constant ratio q. aₙ = a₁×qⁿ⁻¹.

What about 1, 2 and n = 5?

16. 1×2⁴ = 16.

What about 5, 0.5 and n = 3?

1.25. 5×0.25. The calculator keeps the raw fraction.

What does floor do to n?

n = max(1, the integer part of (n)). 4.9 becomes 4. 0 becomes 1 and returns a₁.

Does the result use six decimal places?

No. The calculator inserts the raw number. 1.25 stays 1.25.

How is this different from an arithmetic term?

The calculator multiplies by q. There you add r.

Where is the series sum?

On the geometric series sum card. Here one aₙ.

Does n = 1 return a₁?

Yes. q⁰ = 1, a₁ remains.

Does a negative q pass?

Yes. 3, −2 and n = 4 give −24.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.