The concept of an arithmetic sequence is common to all people and to be more specific the definition of this concept is as follows: it is a set of organized numbers in which the difference among the two numbers is constant and such numerical difference is called the common difference. For better understanding, we pick an example of an arithmetic sequence: 6, 10, 14, 18, 22, 26, 30, and 34. Deducting two successive numbers from any part of the above series will leave us with a common difference i.e. 10 – 6 = 4,14 – 10 = 4, 18 – 14 = 4, 22 – 18= 4. There are numerous applications of the concepts of arithmetic sequence in real life. In this article, we will discuss in detail the formulas for arithmetic sequence along with understanding some real-life examples of the arithmetic sequence.

## Formula For the Arithmetic Sequence

The series of numbers in an arithmetic sequence is in a particular pattern. In the example of the arithmetic sequence that we discussed above, the starting number is 6 which is indicated by the alphabet āaā, and the difference between the two successive numbers in the above series is 4, signified by the alphabet ādā. Essentially, the sequence in the form of letters goes this way: a (6), a +d (10), a+ 2d (14), a +3d (18), and so forth. This pattern is followed in all arithmetic sequences. There are numerous formulas of the arithmetic sequence. Some of the formulas of the arithmetic sequence are below:

- To get the nth term of an arithmetic sequence, the following formula can be used: a + (n-1) d in which a is the first term or a first number of the arithmetic sequence, n is the number of term for which the value needs to be obtained and d the difference which always remains constant in the arithmetic sequence.
- To acquire the sum of the first n terms of an arithmetic sequence, the following formula can be used: n/2 {2a + (n-1) d}, in which n is the number of terms for which the value needs to be obtained, a is the first term of the arithmetic sequence and d is the common difference of the arithmetic sequence.

## Several Applications and Presence of Arithmetic Sequence in Real Life

- Adding candles to a cake each year on our birthdays is one of the common examples of an arithmetic sequence.
- With the help of an arithmetic sequence, we can easily identify a leap year since it also follows the pattern of the arithmetic sequence in which the common difference is always 4 since the leap year comes every four years.
- The increment that we get from the bank on our deposited amount is one such example of the arithmetic sequence.
- In cinema halls, the seats are arranged with the help of the concept arithmetic sequence.
- The arithmetic sequence helps in recognizing different kinds of sequences.

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