Number Sequence Calculator — Arithmetic & Geometric Sequences
Calculate nth term, sum of terms, and list first 10 terms for arithmetic and geometric sequences. Enter first term, common difference or ratio, and number of terms.
Examples:
—
nth Term
—
Sum (Sₙ)
—
nth Term Formula
First 10 Terms
Calculation Steps
Frequently Asked Questions
What is an arithmetic sequence?
An arithmetic sequence has a constant difference (d) between consecutive terms. The nth term is: aₙ = a + (n-1)d. The sum of n terms is: Sₙ = n/2 × (2a + (n-1)d) = n/2 × (first + last).
What is a geometric sequence?
A geometric sequence has a constant ratio (r) between consecutive terms. The nth term is: aₙ = a × r^(n-1). The sum of n terms is: Sₙ = a × (1 - r^n) / (1 - r) when r ≠ 1.
What is the difference between arithmetic and geometric sequences?
Arithmetic sequences add the same amount each time (e.g., 2, 5, 8, 11 — adding 3). Geometric sequences multiply by the same factor each time (e.g., 2, 6, 18, 54 — multiplying by 3).
What is an infinite geometric series?
An infinite geometric series converges (has a finite sum) when |r| < 1. The sum is S∞ = a / (1 - r). For example, 1 + 1/2 + 1/4 + ... = 1/(1-0.5) = 2.
What are common examples of geometric sequences in real life?
Compound interest, population growth, radioactive decay, and the spread of diseases all follow geometric (exponential) patterns. For example, a ₦1,000 investment at 10% annual interest: 1000, 1100, 1210, 1331...