Properties of Arithmetic Sequence
There are some properties of Arithmetic Sequence, some of which are as follows:
- If a constant is added or subtracted to each term of an Arithmetic Sequence then the resulting sequence is also an Arithmetic Sequence.
- If each term of an Arithmetic Sequence is multiplied or divided (not by 0) by a constant number. Then the resulting sequence is also an Arithmetic Sequence.
- For any three consecutive terms of an Arithmetic Sequence sum of the first and last term is always twice the middle term.
- We can observe a symmetry about the mean in the arithmetic sequence.
- An arithmetic sequence can be extended to infinity by adding a common difference to the last term.
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