Arithmetic Sequence and Geometric Sequence
The key differences between Arithmetic Sequence and Geometric Sequence are as follows:
Property |
Arithmetic Sequence |
Geometric Sequence |
---|---|---|
Definition | A sequence in which each term is found by adding a fixed number to the previous term. | A sequence in which each term is found by multiplying the previous term by a fixed number. |
nth Term | an = a1 + (n-1)d | an = a1rn-1 |
Relationship between terms | The difference between any two consecutive terms is constant. | The ratio of any two consecutive terms is constant. |
Common Difference/Ratio | d = an – an-1 | r = an/an-1 |
Example | 2, 5, 8, 11, 14, . . . | 3, 6, 12, 24, 48, . . . |
Sum of n Terms | Sn = (n/2)(a1 + an) |
Sn = a1[(1 – rn)/(1 – r)] [if r<1] and Sn = a1[(rn – 1)/(r – 1)] [if r > 1] |
Uses | Used to model linear relationships or changes that occur at a constant rate. | Used to model exponential growth or decay. |
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Arithmetic Sequence
Arithmetic Sequence is a type of sequence out of all sequences where each term of the sequence is related to the previous term of the sequence by a linear relation. A sequence is a collection of objects where all the terms follow an order or pattern by which the whole sequence can be identified. In the case of an Arithmetic Sequence, each term can be found by adding a constant to the preceding term of the Arithmetic Sequence, this constant sets the Arithmetic Sequence apart from the other sequences.
In this article, we will explore the concept of Arithmetic Sequence and various formulas associated with it. We will also learn about the various properties of Arithmetic Sequences.
Table of Content
- What is Arithmetic Sequence?
- Arithmetic Sequence Definition
- Arithmetic Sequence Examples
- Arithmetic Sequence Formula
- Nth Term of Arithmetic Sequence
- Recursive Formula for Arithmetic Sequence
- Sum of terms in Arithmetic Sequence
- Arithmetic Series
- Properties of Arithmetic Sequence
- Arithmetic Sequence and Geometric Sequence
- Sample Problems on Arithmetic Sequence
- Arithmetic Sequence Worksheet