Sequences Calculators

Arithmetic vs Geometric Sequences: How to Tell Them Apart

An arithmetic sequence adds the same fixed amount to get each next term; a geometric sequence multiplies by the same fixed factor instead — the test is whether consecutive terms share a constant difference or a constant ratio.

How to Find the nth Term of a Sequence

Finding the nth term means expressing any position in a sequence directly, without listing every term before it — arithmetic sequences use a₁ + (n−1)d, and geometric sequences use a₁ × r^(n−1).

Why Fibonacci Ratios Approach the Golden Ratio

The Fibonacci sequence is neither arithmetic nor geometric — its differences and ratios both keep changing — but the ratio of consecutive terms settles closer and closer to approximately 1.618, the golden ratio, as the sequence continues.