Number Sequence Calculator

Find the nth term and sum of arithmetic and geometric sequences.

Interactive Calculator Coming Soon

The interactive version of this calculator is under development. In the meantime, you can use the formula and worked examples below to calculate manually.

Scroll down to see the formula, step-by-step explanation, and FAQs.

Number Sequence Calculator Formula & How It Works

Arithmetic: aₙ = a₁ + (n−1)d | Geometric: aₙ = a₁ × rⁿ⁻¹
  • Arithmetic: constant difference d = a₂ − a₁
  • Geometric: constant ratio r = a₂ / a₁
  • Arithmetic sum: Sₙ = n/2 × (a₁ + aₙ)
  • Geometric sum: Sₙ = a₁ × (rⁿ − 1) / (r − 1)

Arithmetic sequences add a constant difference each term (1, 4, 7, 10… d=3). Geometric sequences multiply by a constant ratio each term (2, 6, 18, 54… r=3). The nth term formula lets you find any term without listing all previous ones. The sum formula counts total area without adding each term individually.

Number Sequence Calculator FAQs

How do you find the next number in a sequence?

First identify the pattern: check if the difference between consecutive terms is constant (arithmetic) or if the ratio is constant (geometric). Then apply the pattern. For 2, 5, 8, 11… difference=3, so next = 14.

What is the sum of first n natural numbers?

Sₙ = n(n+1)/2. This is an arithmetic series with a₁=1, d=1. Sum of first 100 integers = 100×101/2 = 5,050. Famously computed by Gauss as a schoolboy.

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