Number Sequence Calculator · Practical guide
Arithmetic vs Geometric Sequence: What Is the Difference?
Arithmetic sequences add; geometric sequences multiply. Here is how to tell them apart and work with both.
At a glance
The Core Difference
An arithmetic sequence changes by a constant difference — you add the same amount each step. A geometric sequence changes by a constant ratio — you multiply by the same amount each step. Arithmetic grows in a straight line; geometric grows (or decays) exponentially, eventually outpacing any arithmetic sequence.
Interactive tool
Number Sequence Calculator
Enter your own values, then compare the result with the examples below.
Arithmetic Sequence Result
First 10 terms:
Geometric Sequence Result
First 10 terms:
Side-by-Side Comparison
| Feature | Arithmetic | Geometric |
|---|---|---|
| Pattern rule | Add common difference d | Multiply by common ratio r |
| Example | 2, 5, 8, 11, 14 (d = 3) | 2, 6, 18, 54, 162 (r = 3) |
| Nth term | aₙ = a₁ + (n − 1)d | aₙ = a₁ × rⁿ⁻¹ |
| Sum of n terms | Sₙ = n/2 × (2a₁ + (n − 1)d) | Sₙ = a₁(1 − rⁿ)/(1 − r) |
Same Start, Wildly Different Growth
Both example sequences above begin at 2 and use the number 3. By the 5th term the arithmetic sequence has reached only 14, while the geometric sequence has hit 162. By the 10th term: 29 versus 39,366. That explosive difference is why compound interest (geometric) builds wealth so much faster than simple interest (arithmetic).
How to Tell Which One You Have
Subtract consecutive terms: if the differences are equal, it is arithmetic. Divide consecutive terms: if the ratios are equal, it is geometric. If neither is constant — as in 1, 1, 2, 3, 5, 8 (Fibonacci) — it is neither type. The calculator above has dedicated tabs for both kinds: enter the first term and the difference or ratio to get any term and partial sum instantly.
Frequently Asked Questions
Can a sequence be both arithmetic and geometric?
Only a constant sequence like 5, 5, 5, … qualifies as both — it has d = 0 and r = 1. Any non-constant sequence can be one or the other, not both.
Which grows faster, arithmetic or geometric?
With a ratio greater than 1, a geometric sequence always outgrows an arithmetic sequence eventually. With a ratio between 0 and 1, a geometric sequence shrinks toward zero instead.
What are real-world examples of each type?
Arithmetic: saving a fixed $200 per month, or staircase steps of equal height. Geometric: compound interest, population growth, and radioactive half-life decay.
What is the Fibonacci sequence, arithmetic or geometric?
Neither. Each Fibonacci term is the sum of the two before it, so neither the differences nor the ratios are constant — though the ratio of consecutive terms converges to about 1.618, the golden ratio.