Arithmetic Series
The sum of terms of an Arithmetic Sequence is called Arithmetic Series. We use the sum of n terms formula of the arithmetic sequence to find the sum of the arithmetic series.
Suppose the first term of the arithmetic series is a and the common difference is d then the sum of the n term of this arithmetic series is given using the formula,
Sn= n/2 [2a + (n-1)d]
If the common difference of the arithmetic series is not given but the nth term of the series is given (say l). Then its sum is calculated as,
Sn= n/2 [a + l]
We can understand this with the help of the example,
Example: A tree fruits five apples in the first year and at each successive year it has 2 more apples than the last year find the total apple the tree bears at the end of six years.
Solution:
Apple bear by tree in first year (a) = 5
Yearly Increase in apple bear by the tree (d) = 2
Time Period = 6 years
Total apple at the end of five years in the tree.
Sn = n/2 [2a + (n-1)d]
⇒ Sn = 6/2(2(5) + (6 – 1)(2))
⇒ Sn = 6/2 (10 + 10)
⇒ Sn = 3(20)
⇒ Sn = 60
Thus, the apple in the tree at the end of six-year is 60 apples
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