What is the Difference Between Arithmetic Sequence and Geometric Sequence?
🆚 Go to Comparative Table 🆚The main difference between arithmetic and geometric sequences lies in the way their terms are generated. Here are the key differences between the two:
- Common Difference vs. Common Ratio: An arithmetic sequence has a constant difference between each consecutive pair of terms, while a geometric sequence has a constant ratio between each pair of consecutive terms.
- Addition vs. Multiplication: In an arithmetic sequence, terms are generated by adding or subtracting a constant value to the previous term. In a geometric sequence, terms are generated by multiplying or dividing the previous term by a constant value.
- Increasing or Decreasing: Arithmetic sequences can be increasing or decreasing, depending on the common difference. If the common difference is positive, the sequence is increasing, and if it's negative, the sequence is decreasing. Geometric sequences can also be increasing or decreasing, depending on the common ratio. If the common ratio is greater than 1, the sequence is increasing, and if it's less than 1, the sequence is decreasing.
Examples of arithmetic sequences include:
- 5, 11, 17, 23, 29, 35,… (with a common difference of 6)
- 24, 19, 14, 9, 4, -1, -6,… (with a common difference of -5)
Examples of geometric sequences include:
- 2, 6, 18, 54, 162,… (with a common ratio of 3)
- 15, 8, 4.5, 2.7, 1.5,… (with a common ratio of 0.5)
On this pageWhat is the Difference Between Arithmetic Sequence and Geometric Sequence? Comparative Table: Arithmetic Sequence vs Geometric Sequence
Comparative Table: Arithmetic Sequence vs Geometric Sequence
Here is a table highlighting the differences between arithmetic and geometric sequences:
Feature | Arithmetic Sequence | Geometric Sequence |
---|---|---|
Definition | A sequence of numbers in which the difference between consecutive terms is constant. | A sequence of numbers in which the ratio between consecutive terms is constant. |
Common Difference/Ratio | Each consecutive pair of terms has a constant difference. | Each consecutive pair of terms has a constant ratio. |
Subsequent Terms | The next number in the series is calculated by adding or subtracting a constant value to the previous number. | The next number in the series is calculated by multiplying the previous number by a constant value. |
Examples | 5, 11, 17, 23, 29, 35, … (with a constant difference of 6) | 2, 6, 18, 54, … |
An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. In an arithmetic sequence, the next number is calculated by adding or subtracting a constant value to the previous number, whereas, in a geometric sequence, the next number is calculated by multiplying the previous number by a constant value.
Read more:
- Arithmetic vs Geometric Series
- Geometric Mean vs Arithmetic Mean
- Arithmetic vs Mathematics
- Series vs Sequence
- Pattern vs Sequence
- Numerical Expression vs Algebraic Expression
- Calculus vs Geometry
- Mathematics vs Statistics
- Algebra vs Calculus
- Geometry vs Trigonometry
- Algebra vs Trigonometry
- Linear Equation vs Quadratic Equation
- Numeracy vs Mathematics
- Mathematics vs Applied Mathematics
- Prime vs Composite Numbers
- Base Sequence vs Amino Acid Sequence
- Algebraic Expressions vs Equations
- Difference Equation vs Differential Equation
- Numeric vs Decimal