Geometric Sequence Vs Geometric Series
Some of the common differences between Geometric Sequences and Series are listed in the following table:
| Aspect | Geometric Sequence | Geometric Series |
|---|---|---|
| Definition | A sequence of numbers where each term is obtained by multiplying the previous term by a fixed, non-zero number (common ratio). | The sum of terms in a geometric sequence. |
| General Form | a, ar, ar2, ar3, ar4, . . . | a + ar + ar2 + ar3 + ar4 + . . . |
| Example | 2, 6, 18, 54, . . . | 2 + 6 + 18 + 54 + . . . |
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Geometric Series
Geometric Series is a type of series where each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.
Geometric series are characterized by their exponential growth or decay patterns. This growth or decay depends on whether the common ratio is greater than or less than one. In this article, we will discuss geometric series in detail including formulas as well as the derivation of the formula.
Table of Content
- What is a Geometric Series?
- Geometric Series Definition
- Geometric Series Formula
- Derivation for Geometric Series Formula
- For Infinite Geometric Series
- Product of the Geometric series
- Geometric Mean
- Formula for Geometric Mean
- Geometric Sequence Vs Geometric Series
- Sample Questions on Geometric Series