What is an arithmetic sequence?

An arithmetic sequence has a constant difference between consecutive terms. For example: 2, 5, 8, 11 (d=3).

What is a geometric sequence?

A geometric sequence has a constant ratio between consecutive terms. For example: 3, 6, 12, 24 (r=2).

What happens when r=1 in a geometric sequence?

When r=1, every term is equal to a₁, so the sum is simply n × a₁.

Can d or r be negative?

Yes. A negative d creates a decreasing arithmetic sequence. A negative r creates an alternating geometric sequence (terms flip sign each step).

What is the sum formula for an infinite geometric series?

If |r| < 1, the infinite sum converges to S = a₁ / (1−r). This calculator handles finite sums only.

Math

↵ to calculate

Sequence Calculator - Arithmetic Geometric Series Online

Detect arithmetic or geometric sequences and calculate the nth term, sum, and first 10 terms.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

A sequence calculator automatically detects whether your sequence is arithmetic (constant difference) or geometric (constant ratio), then calculates the nth term, partial sum, and lists the first 10 terms. It covers the two most common types of mathematical sequences used in algebra, finance, and science.

First Term (a₁)

Common Difference (d)

Term Number (n)

What is Sequence Calculator - Arithmetic Geometric Series Online?

How to use it

1️⃣ Enter the first term (a₁) of the sequence.
2️⃣ Enter either the common difference (d) for arithmetic or the common ratio (r) for geometric.
3️⃣ Enter n — the term number you want to find.
4️⃣ Select whether the sequence is arithmetic or geometric.
5️⃣ Results appear instantly.

Formula

Arithmetic: aₙ = a₁ + (n−1)d, Sₙ = n/2 × (2a₁ + (n−1)d). Geometric: aₙ = a₁ × rⁿ⁻¹, Sₙ = a₁ × (1−rⁿ)/(1−r) for r≠1.

💡 See it in action — a real example

Arithmetic: a₁=2, d=3, n=5 → a₅ = 2 + 4×3 = 14. S₅ = 5/2 × (4 + 12) = 40. Geometric: a₁=3, r=2, n=5 → a₅ = 3×2⁴ = 48. S₅ = 3×(1−32)/(1−2) = 93.

❓ Common questions

What is an arithmetic sequence?: An arithmetic sequence has a constant difference between consecutive terms. For example: 2, 5, 8, 11 (d=3).
What is a geometric sequence?: A geometric sequence has a constant ratio between consecutive terms. For example: 3, 6, 12, 24 (r=2).
What happens when r=1 in a geometric sequence?: When r=1, every term is equal to a₁, so the sum is simply n × a₁.
Can d or r be negative?: Yes. A negative d creates a decreasing arithmetic sequence. A negative r creates an alternating geometric sequence (terms flip sign each step).
What is the sum formula for an infinite geometric series?: If |r| < 1, the infinite sum converges to S = a₁ / (1−r). This calculator handles finite sums only.

⚡ Related Math Tools & Calculators

Arithmetic Sequence Geometric Sequence Standard Deviation