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Sequence Calculator

Find terms and sums of arithmetic or geometric sequences.

Introduction

Sequence Calculator — Find terms and sums of arithmetic or geometric sequences. Enter Type, First term, Common difference / ratio, n to get an instant, accurate result.

Formula

Arithmetic: nth term = a₁ + (n−1)d, sum = (n/2)(2a₁ + (n−1)d). Geometric: nth term = a₁ × dⁿ⁻¹, sum = a₁(1 − dⁿ)/(1 − d) (or a₁×n when the ratio is 1).

Step-by-step

  1. Enter the Type.
  2. Enter the First term.
  3. Enter the Common difference / ratio.
  4. Enter the n.
  5. Click Calculate to see your result instantly.

Real-world example

Example: With Type = arithmetic, First term = 2, Common difference / ratio = 3, n = 10, the Sequence Calculator gives Nth Term: 29, Sum: 155.

Frequently Asked Questions

How do I choose between arithmetic and geometric?
Arithmetic sequences add a constant difference each step; geometric sequences multiply by a constant ratio each step — pick the mode matching your pattern.
What does "sum" mean here?
The sum of the first n terms of the sequence, not just the nth term itself.
What inputs does the Sequence Calculator need?
You'll need to provide: Type, First term, Common difference / ratio, n. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Sequence Calculator?
The Sequence Calculator applies the formula exactly as calculated — Arithmetic: nth term = a₁ + (n−1)d, sum = (n/2)(2a₁ + (n−1)d). Geometric: nth term = a₁ × dⁿ⁻¹, sum = a₁(1 − dⁿ)/(1 − d) (or a₁×n when the ratio is 1). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Sequence Calculator free to use?
Yes, the Sequence Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Sequence Calculator

The Sequence Calculator uses a real, verifiable formula — Arithmetic: nth term = a₁ + (n−1)d, sum = (n/2)(2a₁ + (n−1)d). Geometric: nth term = a₁ × dⁿ⁻¹, sum = a₁(1 − dⁿ)/(1 − d) (or a₁×n when the ratio is 1). — so results are accurate every time, not an approximation.