Arithmetic Sequence
Define Arithmetic Sequence.
Arithmetic Sequence is defined as the sequence where each term of the sequence can be calculated by adding a constant in the preceding term of the same sequence.
What is the Common Difference of Arithmetic Sequence?
The difference between two consecutive terms of an Arithmetic Sequence is called the common difference of an Arithmetic Sequence.
What is the nth term of an Arithmetic Sequence?
The nth term of an arithmetic sequence is given by the following formula:
an = a+(n-1)×d
where,
- a is the first term of the sequence,
- d is the common difference of the sequence,
- n is the number of terms in the sequence,
How to find the Sum of the First n terms of an Arithmetic Sequence?
We can use the following formulas to find the sum of n terms of an arithmetic sequence.
Sn = (n/2)(a + l)
Sn = (n/2)(2a + (n – 1) x d)
where,
- a is the first term of the sequence,
- d is the common difference of the sequence,
- l is the last term of the sequence, and
- n is the number of terms in the sequence,
What is the Difference between an Arithmetic Sequence and a Geometric Sequence?
In Arithmetic Sequence, the difference between any two consecutive terms is constant. Whereas in a geometric sequence, the ratio of any two consecutive terms is constant.
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